{"_id": "fHaJtr8wLsawDD7Fe", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1:Node | n1 not in adj.n1 \n\t \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "jsMNuibDfZubyvNzA", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:52:35"} {"_id": "LZCt5EfpaJqrceYF4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iiGHdmnt7QXs8SmNC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:51:01"} {"_id": "7qaTQEF6aLv7jQ9Jx", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.(^adj + ~adj)\n\n \n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A5snf38SzPc7avMxz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:21:08"} {"_id": "ZGmoBAzeHgGTa7MN8", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | n.adj + (some Node.adj or some Node.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "2X6FmbS57eZjwZMPz", "msg": "+ can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node}\nRight type = {PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:16:49"} {"_id": "biczctFgZu6RQEWiK", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x,y : Node | x->y in Node and y->x in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vd6DBBmRi3zcQvv5w", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:53:38"} {"_id": "YuB7EKWxC8qiECrE5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + ~*adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "v57GyoZoSAK2W9MQz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:33:49"} {"_id": "ZzpymFCCXzKY2h4Fj", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode in Node.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FhRC5ZhMSE9sRjHx3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:54:31"} {"_id": "RrjezRvC8tWSJMnWh", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "y6KWYG37iJ4E2Dec2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:28:05"} {"_id": "dsPdjsmgwYTZy3dDe", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.^adj\n\n\n \n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 07:34:48"} {"_id": "JqR5W2rBpvTdjCEin", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Y6X5AZw5C6SfxXTqM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:52:24"} {"_id": "Xt3hfcTegHGDo3Aa5", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ydzparX5q7KQvEMXw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:41:08"} {"_id": "AXnkcvMmvmvH3ZvkX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ln9eB7NSTRm2zF97K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:13:48"} {"_id": "mqn2xEuwT2t7gw2sS", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8dEpuEs54fv6SuWec", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:12:02"} {"_id": "9botT8pjnujF65935", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n all a,b : Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uzkJJdBg7rqESLcRS", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 444, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:37:19"} {"_id": "4P2ka4twAetKWYs77", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | ^adj.x in ^adj.y & x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vaD3kGM6DeHKDyuy9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:17:59"} {"_id": "Lai6LmFvk9vY8Hts8", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tlet n1 = n.adj.adj.Node | (all n : Node | n->n1 in adj)\n\n}", "derivationOf": "cbzqec2gZ4cA7FEj7", "msg": "This expression failed to be typechecked line 71, column 8, filename=/tmp/alloy_heredoc1627903148986236163.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:59:41"} {"_id": "xJZX8xEDEQ65s8Wu9", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj.adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jEBo9TcxYCkKDT8B8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:47:06"} {"_id": "MDd7HnFP8nTLPrPNP", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "icqXGmWKzDakAMGmd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:29:34"} {"_id": "BRmexnNjDbauEbFpj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some n:Node | Node in n.*adj \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "Htir3qPFatNzqv9X8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:56:09"} {"_id": "Fn3RwAWEEagpnnqTH", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "2mpJRKeXJt4us4Bwt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:30:35"} {"_id": "2PCmX2bfo7Ac8CJXx", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tNode in Node.(adj.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "87wpMu8MjoCd83XxN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:36:24"} {"_id": "uxMhnWmzsfL5RRxwc", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Gy4tkXTzuphg3PapM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:56:29"} {"_id": "eRqkxP3qxX9rzWcb8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 in adj implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "BQXh7BKCqSEMGKpjB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:04:44"} {"_id": "v7Tf2ffiGwTtbghPP", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n \tall n : Node | no n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Zdpur4T4zacescwTy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:42"} {"_id": "u8z24tqzei93s4Ede", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WRg3upuS5wqHLtPQH", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:41:34"} {"_id": "6sRKNAiAScZJyPxMT", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HQexxqSoXqFQyiPrJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:36"} {"_id": "CsPbiZJrxAcvQb6C7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ShDfQyxvFTQ3tdwSJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:33:22"} {"_id": "tmuJLQNccZMpjdcah", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | ^adj.x in ^adj.y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dNg9JNeaKGMwAKNDv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:16:49"} {"_id": "S3axTLgfc7eGnWZp9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A32phByPhWGeZKD94", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:56"} {"_id": "bbcDBwmcvxtvQb4CW", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hhpNx2JpxveqRpcAY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:17:34"} {"_id": "npJzGCrcecaFZXgyX", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n *adj = Node set -> set Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wJg2qDShKsH7NbHGY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:00:59"} {"_id": "XDW5KJ7FPygeY3hqZ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "idYRhcoxpck7snKRF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:08"} {"_id": "hEAzduJktqR8k95Kj", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a and a->a not in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "529uzPgL5PJpaa356", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:15:17"} {"_id": "7NxrvcYFdF7t5uvEC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n", "derivationOf": "xTiX2NJqkD7WLbtBd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 15:09:14"} {"_id": "wAykBk3paE8MwEWG2", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all n : Node | some adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5L7QrxcPTbnfS3pD7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:27:22"} {"_id": "2TkjxdEo6BKJgr3Wu", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tnot iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fnHT9TTtHEhEGx34p", "msg": "This expression failed to be typechecked line 49, column 2, filename=/tmp/alloy_heredoc847869023020882709.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:46:16"} {"_id": "XdjxKJfTt4A27T3Q6", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *adj.x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PDdWyjL5zf4tPfjyb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 21:29:17"} {"_id": "4oKWsm94d5qrhAdc4", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.^adj\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ZpatMPg7MrCezdAEz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:43:34"} {"_id": "j9Fag4Ertte4Dd74X", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FgDzhyF3aTXZggSF5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:54:07"} {"_id": "udKna2mKaGqhY46yS", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ctwZMgL6HTyRWtLJo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:53:32"} {"_id": "9Pt9srNPrCK4cLgb6", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.*adj + adj.*Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "YuEhrfBtMciYvCK6L", "msg": "* can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 11:27:25"} {"_id": "2R2o526ZPwMMGusRW", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4rJ6C5dg9CXtQxyTR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:18:00"} {"_id": "ZEXea3QQj8vPPf7k6", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected \n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "mBDH9QRXtiEY4PjPA", "msg": "There are 1 possible tokens that can appear here:\n.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:39:47"} {"_id": "FtdSvo7WmeWnmcJsZ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CgyEnyqa9TdQ6L5ff", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:33:05"} {"_id": "4vHfY3JiuPDkJ6oRg", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7a49oq5pimKpPjiXT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:07:25"} {"_id": "HfXvNCbB8bvRYzrRd", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gEzB5ZAjTNBx3zW24", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:09:01"} {"_id": "awA5T6ZL5fZiNN3cr", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n Node set -> set Node in *adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "npJzGCrcecaFZXgyX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:01:08"} {"_id": "S8BRQxkqtg7hLNj4b", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mMGtE38MFg63Szu5W", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:52:11"} {"_id": "ueGyL6TunATaKsi3v", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 :Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n2 in n1.^adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\npred noLoops1 {\n\tall n1:Node | n1 not in n1.adj \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in Node.adj + adj.Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\u00b4\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}\n\n\ncheck {stonglyConnected } for 7", "derivationOf": "oP9CiSswcrkQK95xR", "msg": "Syntax error at the ? character. HEX: \\u3f)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:24:18"} {"_id": "NYuR2BGgEHCmCMyxs", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^adj + b.^adj = a+b\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hNkjHgkLZmH29eio8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:47:30"} {"_id": "DPquTShRiraDHbqic", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "PpP3foJbmGZTNGAzD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:06:14"} {"_id": "Jw3MRXpkbdhxDRgzc", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CSK8qoy3fsWBfwYx6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:20:20"} {"_id": "gShgsFcyQZFcgPxJK", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n all n : Node | n.adj.adj = n.adj\n}", "derivationOf": "EwxvrdFTunfheSAH9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-19 10:50:54"} {"_id": "MDCE92RvDuX7pQHyW", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "naNLfsXErDobYo3ui", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-26 09:21:21"} {"_id": "QcRD5957JiXbxbX69", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1 = v3 & v3\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "o4XqbD2GLKBcQxAEj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:15"} {"_id": "SXq9nd639PYBJj2nq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rJtMY43HNZYp4eZPT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:41:18"} {"_id": "nXtJrkmwFfzitCQ6B", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:07:23"} {"_id": "PQtMTsNnYXg9cpiHo", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\tNode.^adj in Node\n}", "derivationOf": "FGjDcdz3nPpiM8tBm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:31:18"} {"_id": "qzWaHYy5bokmT4TsX", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all ad : n.adj | n in ad.adj and ad.adj in n \n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A6JPPEMcwhQyPSrvC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 01:34:16"} {"_id": "aYdFyn9kLvgexZzMa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj - adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YFga9QdeMJAtyb6wP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:32"} {"_id": "2BQziERmhubJiWgxA", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in Node<:adj\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FfgxwQrEkoESssaSp", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:33:06"} {"_id": "GQvF8Z9JoAeZi33zy", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no n.(adj.~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5nMNja2nwj8iTxWtS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:31:08"} {"_id": "633WagKkvjHSeAMbS", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NXpoLgqq7iYbrep4X", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:24:34"} {"_id": "WzT7soKNczJoh5mjm", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CZHAEYbHRCcf7CXhQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:32:52"} {"_id": "hY5mkiAcGWidRDSj9", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | (n->(n.adj.adj.Node)) in adj\n\n}", "derivationOf": "MNcuF5nL5stFYbGLi", "msg": "This cannot be a legal relational join where\nleft hand side is n . (this/Node <: adj) . (this/Node <: adj) (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:57:42"} {"_id": "HMbgRtqd3ryfRMfd3", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | no a & a.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DXLvwzGzLQyv3JQsR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:38:18"} {"_id": "XbCEGLStzAXbgaGZf", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "9thruSvCn5kvpjHei", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:33:01"} {"_id": "XipvfopivmfLyFwJk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(adj + ~adj) in Node - n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ewvvq5YBxdeyHXJSf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:35:10"} {"_id": "LsjBTyBkXuRkkLsvj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:11:11"} {"_id": "sAdzQFJSAMc5Rt4Wu", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n != n.adj\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8dvDuvQcQi6ueFN58", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-2 23:09:03"} {"_id": "cAEYaQQdzLb8xjmWz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jnTFoHbt9wLsTGLnx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-6 20:49:50"} {"_id": "Mg5YJ4N3qJ4gsgWHg", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.~adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yi4q8osWt2Y7x24vw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:42:17"} {"_id": "qXp933g8sTNhNCaHz", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y : Node | x->y in adj implies not y->x in adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6WzTkSNPuavYnpQwJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:37:38"} {"_id": "jvFFPz6DZkAeHHnrH", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "MdZcTdNNzY3KCeYxq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:48"} {"_id": "HAnaxx4EM5eht5CJC", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1, e2, e3 : Node | e1 -> e2 in adj and e2 -> e3 in adj implies e1 -> e2 in adj\n}", "derivationOf": "7692guzvutgRFyvme", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:32:21"} {"_id": "af8qaAZNKXxSLhHWD", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:47:07"} {"_id": "Pk8FP23qP9fgd8bYR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2 : Node | n2 in n1.adj.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SYPR4PutSoWm523Kw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:56:07"} {"_id": "YkCCzKim7gJLQhfQD", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RLAGpubJ7CM44o9PJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:29:43"} {"_id": "8mmx2eukmRRyi6jTt", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\nall disj x,y : Node | x in y.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "HNuMXgkXgrH9Qwz38", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:40:13"} {"_id": "3NRpaL8Cjh8SdocZk", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "d6uBdw7oYLWekaPkh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:13:59"} {"_id": "LF6vPczykCeGbi9h6", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1->n2 in ^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "gr4C7yKCmpaCCK5LW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:47:49"} {"_id": "yAm7c34v5CLFCSmQF", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a,b : Node | a -> b in adj implies b -> a not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LA5G32WTZrmH9qqHH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:14:39"} {"_id": "gYMAJRWxAW2vbJ56z", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y : Node | x->y in adj implies not y->x in adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6vrXRk772dcHQHH6k", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:37:56"} {"_id": "j2rrRCQSYT5tMW5tH", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "af8qaAZNKXxSLhHWD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:47:48"} {"_id": "MiT55vP4qmnTAzoeD", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno n:Node | Node not in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "D4wywhte7xWsWazSz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:16:54"} {"_id": "TrSqiQaeFLbD3GMGQ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "C7RPm3PBBBgtXNm4J", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:41:04"} {"_id": "jnTFoHbt9wLsTGLnx", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "v5LgvYm7XBDinQ4FF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-6 20:49:44"} {"_id": "fucryhfnSCHjPyt9q", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj . ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vgvhjX2rFd32takzZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-7 19:00:27"} {"_id": "apnPK6pA4c3ibhG6D", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode in adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tECQKhXzhGNN8ToqE", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:17:17"} {"_id": "6dhAEsunh2PpiuwuZ", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | (n2 in n1.Node.Node) implies (n2 in n1.Node)\n}", "derivationOf": "EmreY8shF7ficgSKi", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:48:13"} {"_id": "efkY2hspDKufut8cR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n ~adj.adj in iden and adj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6kAJwj478ZGxdXMbX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 17:50:30"} {"_id": "eFHKYCFYoj5DbffBw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno Node.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w6uiHqoT3Pn5rhGjK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:03:17"} {"_id": "S5pq7ZiYbGTMsmDqE", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tno (^adj + iden)\n}", "derivationOf": "fP9sfgKu7iCYLczju", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:31:41"} {"_id": "fAv7Xhia6YheCzuWf", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in ^n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tZyz73y3ALaLEtD7H", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:51:25"} {"_id": "Ljk3sLYcNBpfc2vgG", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n, n1 : Node | n->n1 in adj iff n1->n not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wt5pKWW4XjEMxa3XR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:26:38"} {"_id": "GmEjxTj8XgWi8jnyQ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "34Ge9bgKKjK82zZdZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:08:28"} {"_id": "4iDSrcAPzSwL6uBG3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.^adj in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "usTK8xxodgCS5oxAk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:28"} {"_id": "rQCt8axSmXekCzjwT", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some ((n1.^adj)->n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "AEo9kSwvd4u6L6kSr", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:53:17"} {"_id": "tifQRriK8AisDwynD", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:45:55"} {"_id": "oFxkzRSAmEueSvyaz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in n.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vTMfggpivgw9Cuo2S", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:27:43"} {"_id": "GSeNSrXG2fYnMi9Ay", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in Node implies n2->n1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-2 10:13:27"} {"_id": "SKXBoTpwPTvubgDaK", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j9Fag4Ertte4Dd74X", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 02:00:55"} {"_id": "NB8aGPsLj453y8ToP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "fCHAuSfR8G55KL8me", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:20:04"} {"_id": "XSrtdPGcD94CurAMg", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "i3g8f7rNJBLq8epDq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:52:04"} {"_id": "NZkpn5acwkzEE6Mkz", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "6qHwqSi3ghZ3SmLot", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 444, "y": 265.3333333333333}, "Node1": {"x": 296, "y": 132.66666666666666}, "Node2": {"x": 592, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-11-21 11:39:22"} {"_id": "6NPn29JkaZkgC9y9j", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x,y : Node | z->y in Node implies y->x in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"z\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:52:58"} {"_id": "oGSQFYZaYwmeWBWhe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "R5TkrAtHvxK5MyWGG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:57:37"} {"_id": "9ky3ZgNdPskrrpPs5", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aEqZ7hEHWW3zRK7an", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:17"} {"_id": "yZSyz9jZaE22KZR2x", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | Node in (x.^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vDDKTrQsrTwnRjwAY", "msg": "This cannot be a legal relational join where\nleft hand side is x . ^ (this/Node <: adj) (type = {this/Node})\nright hand side is y (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:54:26"} {"_id": "nbeRopRNWx9QDt9Nn", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\n \t\n\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \t\n\n \t\t\n\nall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oaiY7tvxF4a7kBXDb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 11:15:35"} {"_id": "3sKtY6YzHQbMqfFgc", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode->adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5neDqD2euJPYPHPzP", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:35:49"} {"_id": "DxEdqk7h4k8THWXXn", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nNode in Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eX7qbeN5LLPuvCp6m", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:28:07"} {"_id": "hmgbtfrgfmiHK9C2f", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\t\n all n:Node | n.adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aKXnxZBN55uB9dKXd", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:05:18"} {"_id": "Qd3kzyBZXXRcbjgtj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a,b : Node | a -> b in adj implies b -> a not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tsome a,b : Node | a -> a in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yAm7c34v5CLFCSmQF", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:15:18"} {"_id": "nd4b7pkrTNGZZJ64X", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and a->c in adj implies a->b in adj\n}", "derivationOf": "tZcdAJzCgbSFLMSnz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:53:20"} {"_id": "ouSfYNs9msZx565to", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:14:50"} {"_id": "DwfaAGREgW47K39G8", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "4zGdc69JmS2d5g6oS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:21:14"} {"_id": "zgazum7dcuty6TcBn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n not in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SzaiuGJAqoCX8FAni", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:17:26"} {"_id": "oSZ7jDNvSRW9faPmL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "qaGr6xZPwyGZkumjF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:53:24"} {"_id": "czGMt537zpWkfBjur", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1:Node | some n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cTounfSycBe8kvTq7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:35:45"} {"_id": "XxPNhQKpnQjvNa3oe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = ((n.^adj + n.^(~adj)) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "ASDgN3J7wW3MEvruE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:59:44"} {"_id": "Za2xfEZq8Q7jjHTvR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj + *adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iPqgmP7YZYBXQZnKG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:50:23"} {"_id": "pB28tDFuQa6987vrv", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | (Node - e1) in (e1.^adj + ^adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tCByNmgELfNEkunCX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:29"} {"_id": "BQ7seeKPK5KczDvzf", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aT982RPaXRfKRz4Dr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:15:44"} {"_id": "QwEjRMZnGetMBayEa", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7QXs37HTyF6si9djs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:35:50"} {"_id": "hkqokrtCX9mJxHdkr", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PCQZGyFgAGFEbSjgP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:27:59"} {"_id": "Ffd3Ce5PCj5wHBWXu", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dAj9fuhg7eMwtbfDZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:17:11"} {"_id": "X3emR4MixF82kmvJv", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + n.*adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Wg33yfez3v4pzKKZR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:13:23"} {"_id": "y5m97H8jwTMrQ5ACu", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.adj implies a in ~a.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5gB4acASY5jnRvzat", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:35:49"} {"_id": "EfgGdQTBZFTDqG8qc", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n *adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \n ^adj in adj\n}", "derivationOf": "8bvioCHwnTs8SEW3g", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:02"} {"_id": "5owgbNrqwQRxQpoGE", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "M5KDoZKgRxZfWSzwH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-13 17:09:46"} {"_id": "fFD6vhLWCMjCty9a3", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9JZ9xyb6JNYYqYdHZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:59:54"} {"_id": "uk2RtKSThbHftbZrp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QxyEwdSYpTxSF2XXj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 11:07:34"} {"_id": "BqeusERjyvWvoTH6F", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RrjezRvC8tWSJMnWh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:28:30"} {"_id": "G7dBYioxFYpA2bxr2", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n & n.(*adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8X4nPngt82SahYyTF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:01:29"} {"_id": "NMH5xSY6MKuYCK73A", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dNzW2ByAgGxdTEPNW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:32:00"} {"_id": "YkszeZJCQaWGe2pff", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hM2qJg7mKRHfQX9jh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:17:34"} {"_id": "iGXoL2tFLaymLQcfG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in (Node.adj & adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "iWYN82N5ApWtWQtxB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:29:32"} {"_id": "WHn2R3XemrY3pyG8z", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in ^adj or iden in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Yf2tyvoDSJN73LBmu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:56:10"} {"_id": "d5W7hroFjBHcdtbf6", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj + ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \t\n\t\n}", "derivationOf": "Dk6pGRMzvsWKR9w8o", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:01:27"} {"_id": "YiGtWYezEk2xTxC8R", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "imacbbAbQ4Sw5fXE2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:12:15"} {"_id": "NWgfpJsNKdLsWAa5B", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in Node<:adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9QCuN5ycjqhNKxWnp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:33:44"} {"_id": "DdQ4k2Gk4kcxBhr9c", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XGD9Hc8iifRRMMNoz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 03:28:11"} {"_id": "DNWm3hqkbuyymMe7D", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ns6GxeNwMeJeu8oPH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:29:38"} {"_id": "MNcuF5nL5stFYbGLi", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | n->(n.adj.adj.Node) in adj\n\n}", "derivationOf": "stynskXSuZ3qvpREP", "msg": "This cannot be a legal relational join where\nleft hand side is n . (this/Node <: adj) . (this/Node <: adj) (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:57:11"} {"_id": "3Q3MX7mdNGrx5xq7u", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode = (^adj + ^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zvFCL8JLxYfQGDLEt", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:34:06"} {"_id": "bmCuNM2yzXW8ScPo7", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | no n->n in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "F4ZfekEfSX438668P", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:08:23"} {"_id": "2zGqPrNkLq8KfmBkj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bWexm3do9Facvimi4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:19:16"} {"_id": "4FgFJfkb3avKQr5TD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\t some adj Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "3hxeenrzJLz43DWow", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:11:59"} {"_id": "HQd862D763tBSiFwe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj + ~adj.n \n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qs2fFKfE7htCc9gSB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:56:35"} {"_id": "umLP8soNCKRirggdX", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:12:03"} {"_id": "XdXPGH3QQTBTyeaat", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj + iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EykLzWSJguJMiwJkA", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:20:56"} {"_id": "ywGH9ATwfP3MjZSNL", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ud37uziuykypA5fbc", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:44:57"} {"_id": "xTiX2NJqkD7WLbtBd", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n", "derivationOf": "tmsLAQp4RrJeFndXy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:08:53"} {"_id": "bBK4KJHoFqYtFA7nf", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "g95DWsmuAQygLjLJQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:50:51"} {"_id": "5gHXhaTQxtWN6wd6d", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "qofWKq8s9XJJK9sSB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:46"} {"_id": "n4RJcfDSwSdZmewkA", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tNode not in Node.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8REsJyjRWqWPqeoh6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:49:54"} {"_id": "JE2ZD87KjZiwc8Ypz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.(^adj + ~adj)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7qaTQEF6aLv7jQ9Jx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:22:05"} {"_id": "sMa67yC6r3FuarjsP", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = not Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2sP62jq5cXaBFuNGA", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:38:10"} {"_id": "NP82CKdPFhkvkCLy6", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node in (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node in (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "rcSKhCfXqAwtWDixQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:54:08"} {"_id": "amvKW3YyJJSzvKEKm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "38bD9AmmEwn5p4Dfd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:56:29"} {"_id": "Z2d6odytdWiSHNDjf", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node | adj = a.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eLnQye7Byy5Zd75CL", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:31:06"} {"_id": "Dk6pGRMzvsWKR9w8o", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x.*(no adj - ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \t\n\t\n}", "derivationOf": "8PYM47huJdYsDZKd2", "msg": "This expression failed to be typechecked line 57, column 27, filename=/tmp/alloy_heredoc2455316261776937739.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:00:54"} {"_id": "t6iHaESFGcGgm4YGJ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "m9rQzonu2a2EYCCWa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:16:12"} {"_id": "whD2BTo3zbGLEH5MB", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MiT55vP4qmnTAzoeD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:17:12"} {"_id": "CMYqbLrLutfghetJE", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1 : Node | some n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}", "derivationOf": "dZQEh6PfskrfYvArB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:18:23"} {"_id": "tkwJrZ339qZerGfsF", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj && ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "abtoGgqxkR7HvzLHt", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:52:25"} {"_id": "RGk73q2rQQNKsZ6hB", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3sKtY6YzHQbMqfFgc", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:35:58"} {"_id": "sWDR9s3zwpeJxJ5ma", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1:Node | n1.adj != adj.n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "633WagKkvjHSeAMbS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:25:06"} {"_id": "RxqvcTJgxcEAxyTvi", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HimAoH6MJGRi7nKmy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:25:16"} {"_id": "25iztATChCq5oDfbi", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "rbsrSDycndWfoLQa4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:52:51"} {"_id": "qaEvt5qs8SvX9d2Zj", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tsome a : Node | a -> a in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QrRi5Bwf7NMknbj9L", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:22"} {"_id": "xiCtTNXk2xNcnDz6u", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HzgA5ju3QfGt6iXXX", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 444, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:40:27"} {"_id": "GZQwdTcqqamdhJDzB", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies no y->x in adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "o6TquqtPqJ4kgWxYs", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 17:52:39"} {"_id": "JpzeCcAXewj5g2Pgr", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6LepbWtvpYsmg9Jhx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-7-8 01:58:47"} {"_id": "kfmijyopnSxnFzdmG", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "LxyJS5kZYhMbtzPiL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:50"} {"_id": "9wPELfwsqAgLqTE7Y", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hgT9v2rwSDbXE9DPY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 18:59:17"} {"_id": "nGqZNwzeAa4CXCfx7", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | adj in n.(^adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cSxKJwM8d8kweoYac", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:31"} {"_id": "8b6jHFB92qD7PXg5u", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kFAgaLyzKiHc2hRJa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:49:06"} {"_id": "8tanQHhqfQDxaago9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^adj + n.^~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7nx7Le6ReWTpREocX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:18:57"} {"_id": "BQXh7BKCqSEMGKpjB", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 and n3->n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "YwqE29ipCpuymqjPx", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:03:33"} {"_id": "fMX3TdAR5kmQusfWD", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "onGQr4M9P84XGEXEC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:11:29"} {"_id": "YuEhrfBtMciYvCK6L", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.*adj + adj.*Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\tNode in Node.*adj or Node in *adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "p9dmJysCpfRCg5TaP", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 11:27:18"} {"_id": "AZMFvgikYEPPNmrxQ", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tno (^adj + iden)\n}", "derivationOf": "BnW433Ax97JfjDGwH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 09:32:45"} {"_id": "y5hk2Z8ArbPDPFRAn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.adj != n and (some n.adj or some n.~adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jju6tLNQ9gJyiiTn7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:10:28"} {"_id": "m4gKLbomsu7LNPgBp", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "xSzfhWXdkfytyqWfe", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:50:13"} {"_id": "4KF4xtozCnahpiZ9n", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bqRNec2J7P4xvEA6g", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 21:22:55"} {"_id": "zJrx2RLx6XFpsb6yA", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no Node.~\u00d1ode\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "rKT4KhpTvDAjZq5hb", "msg": "Syntax error at the ? character. HEX: \\u3f)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:37:25"} {"_id": "ieirnAHTtuNhymNhT", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj.adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SZMrwJLCRnDEwQ59e", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:52:50"} {"_id": "aGgEbJY2BXXPWjLp8", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sHih4z5BbsgN98pd7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:59:50"} {"_id": "mDT3r9m8hptQ3PiHd", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.adj & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Doco3ZyE8xP4iGz2r", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:32:54"} {"_id": "YaYFgNxf5ydQ5f5tc", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall disj n1, n2 : Node | n2 in n1.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qZrWP2WLA2SsfMcxm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:49:56"} {"_id": "bqRNec2J7P4xvEA6g", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "HSiu2LXdf33K69sCd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:53"} {"_id": "PNW43uHJkjFDRiMXB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in (n.^adj + ^adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tone Node or ( all n : Node | Node in n.^adj )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:57:21"} {"_id": "jyESQsmmG8gr8Gact", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node.adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9r6ncm6MBAKGpfCqx", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:30:38"} {"_id": "u7bAiNcusxFDPixhP", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tv1.adj and v2.adj implies v1 = v2\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JTGaYNvyhYWBMDwCj", "msg": "The name \"v1\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:22:40"} {"_id": "ng5PBvy4P3Wah4B7f", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SLXuxNSmnvWmExdF6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:32:57"} {"_id": "MF5wp6YMqE9KzPoa5", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:35:27"} {"_id": "QauacChiRXCxBirFw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "tYgPqWEnpu63DMvfp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:31:13"} {"_id": "AQ5rKKddAQSJ7SXYm", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x & (^adj).y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "R5tmP64DTv5aHmSLj", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:12:13"} {"_id": "DCw4pbPrgdRHyA9F3", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "n4rToR6dp8e9zMcAG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:56"} {"_id": "GTR5sTBzz6gyv3Ku7", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 implies n2->n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-7 20:09:01"} {"_id": "cFT5gsGrXhzHpRXaL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t all n:Node | Node in n.(n->(n.*adj+n.^~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "3ShuzixxvWerSAcjx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:04:05"} {"_id": "J6LwfcjGNQain3oEo", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "8wnpiTcHwwodnGuz4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 22:31:59"} {"_id": "cZ7oq9JJakFawfDnw", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "PhFKeQ7Jt9ud8tE9o", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 23:04:59"} {"_id": "DjNcQfRksZMMfJcj4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in ~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tiden not in ~adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\tadj = Node->Node - iden\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "pAaAuLNNHX6uhNGsu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:27:50"} {"_id": "HdDLRGizwXb74DYFE", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "25iztATChCq5oDfbi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:52:54"} {"_id": "4NEcnKQaMqpQs6bnA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in adj.n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WmeCC5ZNPMP6BGFLW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:40:32"} {"_id": "KYyW3odtGFuXJHhnC", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "iwspqeJdQb4aHuhbZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:18:38"} {"_id": "eHSj4hDRMwnQWs3mh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj + n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "NMRESLs78RoQBXhNk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:44:52"} {"_id": "hnprhndmDXi6CzHkf", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "4vHfY3JiuPDkJ6oRg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:09:06"} {"_id": "dnAw8iqyumxv6i7tH", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^adj + n.^~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6yJgP9tWfingkgcPD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:08"} {"_id": "FSPMPfnmsWreHsSB8", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a,b,c:Node | a->b in adj b->c in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tMkF9C5XqtrcYgi97", "msg": "The name \"b\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:13"} {"_id": "qsuKgTPwMBLsrK6Lj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno ^adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YNSYTHgqvKXDTwKsh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:14:31"} {"_id": "uTtBRnAbhjydQzPra", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in (^adj - adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LZCt5EfpaJqrceYF4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:51:16"} {"_id": "RPLagYXAg54KSZph8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:39:45"} {"_id": "3ShuzixxvWerSAcjx", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t all n:Node | Node in n.(n->n.*adj+n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "fE24Yithtf3YqobJf", "msg": "+ can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->univ}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 12:03:53"} {"_id": "SdHweCDuCZsd546eA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + n.^~adj + n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "GF6wp6miXvF2krEbF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 11:54:46"} {"_id": "nBENvqhqEjPSjz92p", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5owgbNrqwQRxQpoGE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-13 17:15:22"} {"_id": "ayd6NMHctmx46aw2P", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "KgJXFQSfEHd9GE5oR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:40"} {"_id": "H3r2THyfX2hfNvroy", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n->(n.^adj) in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall n : Node | n->(n.^adj) in Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "Zpqzxa7sswfKQD2xd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 02:36:38"} {"_id": "itHwL7EyfKM27usff", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "JbgscHTMywPKQvfqh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:20:42"} {"_id": "uAPbZLx8pNcHLfAnM", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Pik4BGKG99WwjhtBd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:02"} {"_id": "qgL53DYioaNMyxsYd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tundirected and all n:Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zkoSjFR4fiSksxrL5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:55:14"} {"_id": "terRirKfDFWsodEMk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | b in a.^(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "wvc8s6bLfBHiDxFAP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:04:17"} {"_id": "8zBm5ujTgJcCHDacz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 in adj implies not v1 = v3\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9rNbmi4J6yZNSzoGt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:21:38"} {"_id": "ezxTomCd3rzqyyt4c", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "DCw4pbPrgdRHyA9F3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:58"} {"_id": "3MKXFKnNoZj6nrbDu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5YcrfC6q9z3ioZrpK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:14"} {"_id": "YHSXicX4jb7EcvJHv", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8XQSdXgRSvhihY3mw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 10:58:01"} {"_id": "PGnREotvzzguDXnay", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6BKachDG2d764LHCm", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:29:21"} {"_id": "HnphgZRakmZJYEjAT", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SNedL2rPSv3B53tzx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:09:30"} {"_id": "KsCsTSheNYehn5ose", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "E97Fd7qibkcDPdyXa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:47:31"} {"_id": "bY27MLchgYqMaRZ6C", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ezp2zb2gXEHT2RD7h", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 444, "y": 265.3333333333333}, "Node1": {"x": 296, "y": 132.66666666666666}, "Node2": {"x": 592, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-11-11 21:31:05"} {"_id": "3KqtshyXcyf2n9Bn4", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AbErnEiw4edEmokSe", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:37:31"} {"_id": "Gcdq8LaLo2JdeNFYq", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vGJXLqysWoNMNtctu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:39:13"} {"_id": "ZjvFk4CHyKXWjZKm2", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5hcHn2cwnhXNZ2uZD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:43:47"} {"_id": "bymtPQKtZN7RzTuZb", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in ^adj.n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "HPxeXwBMKnBRJZx8W", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:36:13"} {"_id": "mGm93hjBENmed3aJY", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (n.adj.*adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zTWzN39t7RqEMNozw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:45:46"} {"_id": "49ZFp4iMqv2eGczy6", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n1 = n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rFQPzb23E9idiGsSd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:41:54"} {"_id": "AZpmKxyPwuRosGSaj", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.adj*\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ybenavRB94onozjkp", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:32:26"} {"_id": "stoQktpRdp2PCwdRS", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YMhCjQGHg8yGjFhi6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 13:29:02"} {"_id": "QPYiym6jdDhuGf9ww", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:37:34"} {"_id": "Wq23upqnFa85q3kma", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.adj + adj.n).^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "A8A8aaHhay2dKRo5m", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:27:00"} {"_id": "Mde7E2rPj9bdvDtCp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2 : Node | n2 in n1.adj.*adj and n1 in n2.adj.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Pk8FP23qP9fgd8bYR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:58:48"} {"_id": "8oJySioGsgkT2BgMP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + n.*~adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "X3emR4MixF82kmvJv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:14:09"} {"_id": "e2cC3t9dwbriQ4kti", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tnot Node.aj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YsBn949SBMjp9H67S", "msg": "The name \"aj\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:44:36"} {"_id": "JJ8kCGY9ChWvX3juS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^(adj + ~adj) + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | (n1->n2 in adj) and (n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "fAX6ecdeNRcyjZdJu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:44:53"} {"_id": "2ZNrNbuwoNj2hExfT", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | some Node<:adj & n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3waQ5SEc4nnc9tHaj", "msg": "& can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:35:00"} {"_id": "p2jqAZ5aCAkHLS2yJ", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hHnevD2LDhipiXwBJ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:00:24"} {"_id": "ypJiWXCAhifCPFJNq", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ezxTomCd3rzqyyt4c", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:01:01"} {"_id": "JYH9Knp36mFjwWMHz", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "ewYyLf4tni4T2kGbs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:32"} {"_id": "aKXnxZBN55uB9dKXd", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qyPwwCQniJrTDqCzA", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:04:55"} {"_id": "JvLwKxJkMfzoFq7CP", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KworHaSCqgMoJo9QE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:19:40"} {"_id": "FG3Jn2wqNuxkEfbt2", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ey8SDWKQMa46cqumX", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:48:41"} {"_id": "ithXeBTGPiCrMzqhX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | all a : n.adj | a in n.adj implies n in a.adj\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "g3FzjJiims86WNLLA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:33:09"} {"_id": "bMNacyma6W8ueu5t8", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n adj.~adj in iden\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Q5CrYbL4ZS94tg83v", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:15:36"} {"_id": "k9gF87qQ8f3auxQRK", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n, n1 : Node | n->n1 in adj => n1->n not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ljk3sLYcNBpfc2vgG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:26:45"} {"_id": "P7E6yxJmuvL8BcnoT", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1.link.n2) implies (n2.link.n1)\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Q9wkNLFMkwi9H2RYz", "msg": "The name \"link\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:52"} {"_id": "ZF5qBnHmB3gbokaZi", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 21:57:23"} {"_id": "oPmkyJKEmcrWt2u9y", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tadj.adj in adj\n}", "derivationOf": "szERyomfDbJcudyf3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:35:44"} {"_id": "ohkjRKcXm6tYj6smv", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cb2nuCshcwujf7WwS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:20:52"} {"_id": "2ik4jWhnqBYAia4AJ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj in Node.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YeLDB6LTzxiu95jNh", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:08"} {"_id": "tYgPqWEnpu63DMvfp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "xmRwm8RC7r2DENJtg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:31:10"} {"_id": "ZD5RPTo6usJzwvhms", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TfTyWDgvN3kuGctCe", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:22:50"} {"_id": "yyaQ24NMcJ2DnnCa9", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fv2gdbo7sqoaio7i6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:51:06"} {"_id": "NCnciAYCjrX3a3h7q", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vfnxZc3NdxGex724s", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 19:01:53"} {"_id": "BhgAvdrLQuK46tzK8", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vDSCWDH46cSoYvNeE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 10:15:14"} {"_id": "Rds2gfnQ7xccg83u4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NQfzD8KnDFPSedErb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:34:02"} {"_id": "RbPtKzSxxzFhMdMYo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \n \n \tall n:Node | some n->(n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "NYuj43BdvHtHYv4RP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:05:31"} {"_id": "5ukA2Z4mHcsR79Gvk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bY5gCvYEiAuWDgdch", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 11:33:00"} {"_id": "fP9sfgKu7iCYLczju", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tno (^adj + iden)\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:31:30"} {"_id": "x5v3RhfkZQjc9eEZP", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no adj & iden\n\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "asMF7qME7YJkCkKhL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-2 23:22:55"} {"_id": "QjDhvEY2vf4SHEwi2", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno adj.Node & Node.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "quZJs39KSdL3Hm85b", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:29"} {"_id": "Etb7DTZG8a8SKs26o", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n adj = ~adj\n\n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4fJnqKTsPyLTgzXz9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-2 23:39:25"} {"_id": "HbvN8v4WceR2De7RC", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n for n : Node | for a : n.adj | n in a.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sicFqLm5zaJqmFcWN", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:29:57"} {"_id": "qQubEMmJyjqNMCSqW", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G7dBYioxFYpA2bxr2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:02:14"} {"_id": "2za94DXtwqCpwajm2", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | adj.n not in n.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uCmGoqB7XFk3a63ou", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:09:26"} {"_id": "rJtMY43HNZYp4eZPT", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "czGMt537zpWkfBjur", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:36:51"} {"_id": "B9FQ2Zay8vpuAEKGf", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node = adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "HSJfPA8MH4EPfqcZD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:15:18"} {"_id": "6LepbWtvpYsmg9Jhx", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-7-8 01:58:43"} {"_id": "vzuMpX3aAWpHYJJSB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TWQq2qmmjWeQPRK9R", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:28:12"} {"_id": "uCmGoqB7XFk3a63ou", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | n.adj not in adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CW6MkyQnecLmE5ahk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:09:13"} {"_id": "A8A8aaHhay2dKRo5m", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.adj + adj.n).adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "3FqDiJTLs6RWayKbt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:26:54"} {"_id": "hM2qJg7mKRHfQX9jh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WBGiosGJ3KYhAiZJZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:17:19"} {"_id": "vXWvjYDygKcYWG24L", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + ^*adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GugpvZTKKMDbFP9Nd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:52:46"} {"_id": "pxZz94kZxLodX2mei", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a:Node,b:Node | a->b in adj implies not (b->a in adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sNab5R3TRADMgZCAC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:14:23"} {"_id": "oafetzhayxbdDEhGR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t lone Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3vFojw3DS3hpKTGh7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:22:49"} {"_id": "4P5bRM8PADcpyPfAE", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "mnTxyTRX4aKnRZjJM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:41:55"} {"_id": "dNg9JNeaKGMwAKNDv", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj in (^adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YM2pzGASNpwdBzyMv", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:57"} {"_id": "6h2er7TT3bYnJ46LW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\tall n:Node |Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "gGFPZu3t7P3vEALnN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 13:42:36"} {"_id": "sh7hpo9SfYjgwzitj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n.adj not in adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ajdnwWQxbxa34GE9s", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 01:25:12"} {"_id": "ckfpPgKf38rx5BmDw", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JHshE5CMinqsWFQH8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:07:56"} {"_id": "GMGBYPFT5NrbTqhpS", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tadj\n}", "derivationOf": "anKqfNMJp9CyET2fn", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 13:43:00"} {"_id": "6zxhzYDm6PRMi5Azs", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in (n.adj) \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kCYgMbuarW7cc7b2W", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:28:58"} {"_id": "pAaAuLNNHX6uhNGsu", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FG3Jn2wqNuxkEfbt2", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:48:47"} {"_id": "yzqzey5Jt2SBL9snj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ~adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wjYrMphYCA6J39m4y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:32:25"} {"_id": "2da6gvc3CmKm6SutH", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj + ~adj.n + n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "j9xfyw3hJQyZ6hpyn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:59:01"} {"_id": "qFzsh8K7e6rCrZnvD", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj and y->x in adj implies y == x\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YhkotaN8waKTT3cDi", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 17:54:33"} {"_id": "BnJN3MYs67Z3ggWi4", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(adj + ~adj) = Node - n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cmSeTjNiK42fW6KS9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:03:40"} {"_id": "h6C22aYtn9JbkXd6B", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "NCnciAYCjrX3a3h7q", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 19:03:23"} {"_id": "qshSadCvEM8jWxnqn", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "634AjmmYQMvGD56bm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:18:38"} {"_id": "LA5G32WTZrmH9qqHH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BWjdeX8C6Jdhpa9xC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:13:05"} {"_id": "Bn3r6qQ7T2CJwrZNo", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n adj not in ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "N8ZgFyTzQJgfDni7a", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:48:07"} {"_id": "vDdunHBzx28eHFK5H", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "S7DsEc6RFAv8icrdh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:55:48"} {"_id": "SwK2To457So9W495A", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xqpuoBSRuwJiXZNgZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:22:34"} {"_id": "YMhCjQGHg8yGjFhi6", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in adj.n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "t8nGNEt5rnKCfqQP2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 13:28:53"} {"_id": "GkrAHoaDqzwmWQWRN", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj.n = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n : Node | n.adj.adj in n.adj\n}", "derivationOf": "xLmjrmtTYAtHw3QJC", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:35:51"} {"_id": "A3DfRnxryfc7pjzYA", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zvZB5xQPSrHoT3pQn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:14:34"} {"_id": "3EBDauMJyEdjCStte", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\tnot lone Node implies Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "JRM79kRj5wrJ7PvDo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:17:39"} {"_id": "2hX4dZ3WZ476jYh5T", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yGYnKyNKHeJ8jyuss", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:54:03"} {"_id": "LxyJS5kZYhMbtzPiL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "tkqyY4cPSxJd7b6oi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:49"} {"_id": "3tv3aioKHxLBTpCtE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "uRERRoinNqPhyMqRo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 11:14:18"} {"_id": "KTNCkrS8LSbuzPwbf", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mGm93hjBENmed3aJY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:46:54"} {"_id": "aBsYSu2nSoTBzHZYa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "HALkfvTvfWNiWD25b", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:28"} {"_id": "pigaqdHEQKX4rwpme", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj - ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "L6ms2nzPhmPsb4xsg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:30:13"} {"_id": "Pn4QAqeqAqTtzLHme", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "e96iKosoZJnPHvoKf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:14:08"} {"_id": "mG6LXsvtRcfqivNjK", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "3Rd8SwjDBtdFC2mtv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:45"} {"_id": "EdFn4uPy7jJsQhNBc", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "gFXTLrLkAXn7KgbSp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:09:46"} {"_id": "naNLfsXErDobYo3ui", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-26 09:19:49"} {"_id": "2eGnbYnw3Da3B2Nzf", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qshSadCvEM8jWxnqn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:19:10"} {"_id": "RxQMr9oHxBGpgjq5S", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\tlone Node or Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "bsieDb5fiRJc5amPW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:12:55"} {"_id": "AcD8ckn3FwJ9QKj39", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "vzMgGsfTYnk7X4pz3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:31:59"} {"_id": "FofspWqsiWAS2Jy6F", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "NB8aGPsLj453y8ToP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:23:27"} {"_id": "wwAsZiim4hmxSeXe8", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | some n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CAH6AbzRogDRAJ8FP", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-2-3 00:18:28"} {"_id": "7Wft8kg9xfbeuAsxD", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | a.next not in a\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GnRMhShBAp6i3uyjG", "msg": "The join operation here always yields an empty set.\nLeft type = {this/Node}\nRight type = {Int->Int}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:15"} {"_id": "oKNyi3jGBjDFAnCkJ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sg4wa6ELs5vwDR3dp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 21:58:16"} {"_id": "cxC7awE96zEcMjoSN", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x, y : Node | (x in ^adj.y) and (y in ^adj.x)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | (x in ^adj.y) and (y in ^adj.x)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NSnfyuq2kkzuJagCY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:19:23"} {"_id": "e96iKosoZJnPHvoKf", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:13:48"} {"_id": "32iEyg6joWDg5aZPy", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3TmBTsntP9tZgK8GZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:21:33"} {"_id": "ejMnEXJL2Gs4Yd2cW", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden & adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gYF9E5GyDFjFxxHF9", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-12 10:58:43"} {"_id": "e5PiXNEdeSWdTh5Cp", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj \n}", "derivationOf": "JxFth7dBQhinnr53C", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:15"} {"_id": "aQwx7dtLjQ8ooMMCA", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nno ^adj & iden}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KKY2Gg9nAsaeXayH6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 11:13:34"} {"_id": "2nFicSBQcobiTsGy2", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(~adj +adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.^adj+n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pEi8hiTALqGtCfi7D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-7 12:29:03"} {"_id": "tuBxkQuHakxtCFkxX", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n one Node or (Node = (Node.(^adj) + Node.(^(~adj))))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n one Node or (Node = Node.(^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "hhsfxaenckZEp7mS6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:44:01"} {"_id": "a9PJLFq8sXcpcWvJi", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n ~adj.adj in iden and iden in ~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gLN98Daky9TjK5t89", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 17:51:27"} {"_id": "Zzj4jm3frKaN6eKJk", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 20:13:33"} {"_id": "ocvo2sw4pJ2opccAT", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj) = (Node -> Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TKoWGrpZ5Rw8SuYX2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:16"} {"_id": "HpyMJenJeoyZPikb6", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj + ~adj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hZwMRge4byE79Bx9F", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:42:54"} {"_id": "AnAm6jSq8KLPSrEyj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "wpx4upTZmPmNrR7yK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:53:40"} {"_id": "N8qmnKsdbRpwPi2k5", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a => a->n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:33:46"} {"_id": "A63Epaomb4dSL2TzW", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n: Node | n.adj.Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "PPQp35Wdo7dctLF3h", "msg": "This cannot be a legal relational join where\nleft hand side is n . (this/Node <: adj) (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:13:56"} {"_id": "Zdpur4T4zacescwTy", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n \tall n : Node | no n.Node\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qFA8fmf3C7m65AuQr", "msg": "This cannot be a legal relational join where\nleft hand side is n (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:16:21"} {"_id": "JTZBzLBZKbQzqrccp", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aYnx62NPZpXKoQzF5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:26:09"} {"_id": "E3S8NsPbBxwT3ivGy", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = n.~adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AfwhyotybjQAbnmMK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 11:44:29"} {"_id": "73GbJNnQokqwjqPmq", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "Dif6vFzczyuPEvmPE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:24"} {"_id": "cmSeTjNiK42fW6KS9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NdPEcYSk7iL6B5cQC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:03:11"} {"_id": "zpTCjvjCbWxB7fq5x", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall a, b : Node | a in b.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yQticP4FgZANS5ino", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:55"} {"_id": "Lsgxeeu7a4ymTcMEF", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MB6CQ5HBfdMLPuTnT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:02:23"} {"_id": "vgeMnJqZ2orM3dTXF", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n \tno adj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JytpjETstMNBorg8j", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:14:27"} {"_id": "Mkod7Kkjvmh3rahr8", "cmd_c": true, "cmd_i": 4, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "yd6u8QnwgsKCEQdwX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:26"} {"_id": "FDFDfLb7q86iH9Ma2", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n : Node | some n.^adj \n}", "derivationOf": "CMYqbLrLutfghetJE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:23:50"} {"_id": "Z6b9MoyiYgJoBBbuQ", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pFa5LMztKScJNZkhE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:10:33"} {"_id": "mX6NcFoGrkrJcW9EN", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n.adj != adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5bgfCeRgSQNMyoT52", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:26:03"} {"_id": "kDfpgKtBG4qEjhCdd", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tn,nn,nnn : Node | nn in n.adj.adj implies nn in n.adj \n}", "derivationOf": "h9JbLnCXDK4kwWqXF", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-8 19:58:13"} {"_id": "E3QoLfYrj8vgwfpHm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node-n in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Pip4TSfDsqpK4u9oS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 13:43:07"} {"_id": "S4L4nGB2x8u56NTQW", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tcomplete and oriented\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n\n", "derivationOf": "kapz5CR8jaADwoFPo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:17:09"} {"_id": "5hcHn2cwnhXNZ2uZD", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Mg5YJ4N3qJ4gsgWHg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:42:23"} {"_id": "R9L9HBJC33gHNpy6C", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "keb3kgu6Sfn4kQY5r", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:04:57"} {"_id": "JTGaYNvyhYWBMDwCj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1 = v3\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8zBm5ujTgJcCHDacz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:22:06"} {"_id": "vTeWhGrvK2odyLep2", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n,o,p:Node | n->o and o->p in adj implies n->p in adj\n}", "derivationOf": "X67cZA6aocQJvrwRw", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:35:02"} {"_id": "MdZcTdNNzY3KCeYxq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bY27MLchgYqMaRZ6C", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:46"} {"_id": "xabLPGXDa2FNci4R6", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hkqokrtCX9mJxHdkr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:28:22"} {"_id": "MMtz5hFfvLqb4pBvv", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P4ZW9ixC47KY7Zue5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:08:40"} {"_id": "Rjymaeqx75Ncix7mL", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n | n->n not in ^adj\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WHn2R3XemrY3pyG8z", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:57:11"} {"_id": "FxdGN6eMz4xrKwptu", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + ^~adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vDdunHBzx28eHFK5H", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:58:48"} {"_id": "fx3DPNGmAys3urmbo", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n^.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yHqYBLWznWCADtRf8", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-2 10:32:10"} {"_id": "KrYCZmzMR9XNYeixR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:44:52"} {"_id": "h9T7DZqKkydk9qzBG", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "S5spq8hq7vrNc29nq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:35:39"} {"_id": "hgYHQfLso9zNmZ5ft", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & -adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pxZz94kZxLodX2mei", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:11"} {"_id": "XZwpwX85z6f2Ytwzx", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t+adj = (Node -> Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gipF97YGsCnTQLXHX", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:23:03"} {"_id": "FCTuGJwv8niMvk4n2", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1.*n3 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "X4gRNPjWA9B7M4rNJ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:00:02"} {"_id": "GavfJWsg8Cp968xvD", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node -> Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v1, v2 : Node | v1->v2 in adj & v2->v1 in adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6kJwk6zYhFvqwydm4", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:53:20"} {"_id": "4JHzSK2TyZjrmeEA5", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no (^adj & iden)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \n ^adj in adj\n}", "derivationOf": "EfgGdQTBZFTDqG8qc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:29:14"} {"_id": "rt9ppwhyZYu3QHYsC", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj \n}", "derivationOf": "Rw8By7sCc6EBrZzh3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:06"} {"_id": "vwQy2EBKajWBWsLYF", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n : Node | no n.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xWAz95PCxZhS5Zeqo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:27:28"} {"_id": "nuQDhXrF9MCmiiQaJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + ^adj.x + x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oNHxcqHm5NbPSEz4z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 20:51:20"} {"_id": "M88EMg5QBDD4qF57d", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GNfyFrmtT2a92hRCK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:30:01"} {"_id": "wjYrMphYCA6J39m4y", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "v7x3XZ9RkQnhu9YE3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:31:38"} {"_id": "CZHAEYbHRCcf7CXhQ", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n.adj not in n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rjtQWe94aCSkZvFno", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:32:34"} {"_id": "xLKjGE4D7ERNY6B5E", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a,b,c:Node | a->b in adj b->c in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FSPMPfnmsWreHsSB8", "msg": "The name \"b\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:30"} {"_id": "nWkiWCejAYftEhFg2", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9aYhTs3pGkZX2r5Lx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:38:50"} {"_id": "sYYvm3ofYQjsnFeD6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-12 19:15:40"} {"_id": "FzGfXJ3h3CXyoNRCh", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QwEjRMZnGetMBayEa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:35:58"} {"_id": "ggn8uw9QnwYLq2rRm", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno ^adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DtMn2H7krDJXyqnPD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:22:56"} {"_id": "7Pjck9mQNQQJXyq52", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-27 11:01:29"} {"_id": "BmzmTtYqWR9aCKYji", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + ^~adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4iauYf8qgxfMSvfCs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:55:15"} {"_id": "CW6MkyQnecLmE5ahk", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\t\n \tall n:Node | some adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yYJtRJZqFpTWRDBmz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:05:38"} {"_id": "cJgBvQvwiXHRaKjwg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+^adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uQNEWC3vtdLfyESsp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:20:37"} {"_id": "pHgxJZh8Fk6kNbrcv", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oJShrDP5qiBm3WQ7e", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:14:49"} {"_id": "w8L88t7vRmAJWbEzx", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (Node.adj & Node.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5T6nZXZHuEDzrPzfA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:09:05"} {"_id": "EAsGqsyYBuPMAiwHP", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Lsgxeeu7a4ymTcMEF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:10:36"} {"_id": "LPoxXseMHWRiFmAyN", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9sMuGuqDLcTQawBtT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:39:45"} {"_id": "KaDCBCXwAskT5Jj6W", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj implies not (v1->v1 in adj and v2->v2 in adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tkB5XvCZ5GfSsasdg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:28"} {"_id": "PPQp35Wdo7dctLF3h", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n: Node | n.adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "CN2Z4RDRi5yWR9QwN", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:13:51"} {"_id": "teutyHCcW47HNKYjN", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "4pDiLoTkBxGXFep8M", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:15"} {"_id": "YPScjHeMPGASBn982", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj = iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nvvfESNDHkwibFcMj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:00:40"} {"_id": "TqthQbJFSpEA7LGY5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZNczwQrYXGdquPLj5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:42:21"} {"_id": "iiGHdmnt7QXs8SmNC", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in +adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LG4AMnJG2jBdxPpdX", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:50:55"} {"_id": "JS6KFrbJYDYt9o3rc", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "JvMdXe89FhMtr8jra", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:38:50"} {"_id": "6vrXRk772dcHQHH6k", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y : Node | x->y in adj implies no y->x in adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qXp933g8sTNhNCaHz", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:37:49"} {"_id": "RAck4rpyTeCvC6RC2", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in n.(^adj + ^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "gkQACPvPKBt5h82dG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:44:03"} {"_id": "a2vqEGaHnm6Dn86Z9", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in Node implies n2->n1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 21:26:23"} {"_id": "Ysq6bLXeTeyspMCGQ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + adj.x \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QmtwQAx2LSKPzjpeB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:42:03"} {"_id": "5neDqD2euJPYPHPzP", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n->adj => adj->n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "N8qmnKsdbRpwPi2k5", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:34:04"} {"_id": "3TmBTsntP9tZgK8GZ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | (Node - n) in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bfXFuAiREEWrZfzg3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:19:53"} {"_id": "zX4pnatEipZ4ffc3K", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tNode not in Node.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iH2Tn53saZrzn5QGa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:50:16"} {"_id": "eLtxMYf3t4wfpDN9k", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | a->a not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a,b:Node | a->b in adj or b->a in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dtEBNprChrYJpXnvH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:58:46"} {"_id": "pFa5LMztKScJNZkhE", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^node & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w8L88t7vRmAJWbEzx", "msg": "The name \"node\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:10:25"} {"_id": "WgBRZ6sStaqR2Hv7J", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall n : Node | n not in n.(^adj) \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RAZuv6tKSzqFkpybQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:19:21"} {"_id": "WjT9HvSnLmBiWMi3y", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | *adj.n = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CHzj7xdj3YA9itKex", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:19:38"} {"_id": "5Fc23AsRfwMscyFPv", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj != ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xiipBcBE3cSQRgELp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:00:21"} {"_id": "aHD3aNG3pxnjpdizt", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qqRNpidats9s8J74g", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:45"} {"_id": "kbNxrzRWqwBdmBPyh", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "n4RJcfDSwSdZmewkA", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 04:50:24"} {"_id": "FbzJPd278u6HPBbps", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3NYoc8CZYTSWcfLGr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:19:19"} {"_id": "feaFCRx4FFbhXXB5x", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tsome n:Node |Node in n.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "Bf2Dyx9ppecSdS9iu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:37:41"} {"_id": "bZDpu99i2QXmsPpvs", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "9NfRcHT3Tx7gQqBFG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:34"} {"_id": "ufcq4qkq5RMwfXZaS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node) + (n1.^adj:>n1)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "hvBGucb8ERYXibtBL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:29:32"} {"_id": "7FWhprWJmqF3vn2kT", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall n : Node | no n.^adj & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Rds2gfnQ7xccg83u4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:34:43"} {"_id": "HxTSxReiumnp9kkFE", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "vmB7CurmsH88huLJC", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:04:55"} {"_id": "KePxi2WNwz2aP5u3z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x.^(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "bBK4KJHoFqYtFA7nf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:52:05"} {"_id": "qbAqKPPfhnttXsrFQ", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n: Node | n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "LuFp8vs9QrsC6R8qn", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:08:35"} {"_id": "7a49oq5pimKpPjiXT", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oEHtob9zjZggke79q", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:06:30"} {"_id": "Y4huvwtn8bjGD25D7", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "J78k7z84nF5H7947y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:16:03"} {"_id": "tur86Kb8rexN2NnjZ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tundirected and complete\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n", "derivationOf": "FGN837ePK2vfwPhSM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:15:51"} {"_id": "eEQj6xGAuPE69H4Nr", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "jvFFPz6DZkAeHHnrH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:50"} {"_id": "rsqQiavx4XQCmMz6n", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node |Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n \t\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall disj n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj\n}", "derivationOf": "q6RdnBX3g4wje58Db", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:48:39"} {"_id": "A5snf38SzPc7avMxz", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.(^adj + iden)\n\n \n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "55Ssa7ymvrmGBEAdy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:20:55"} {"_id": "8meKbJeFuZ3zM6zR7", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n1,n2 :Node | n2 in n1.^adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uAPbZLx8pNcHLfAnM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:16"} {"_id": "BjHxAfy2eubvQi6DR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n some n : Node | no adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "R2gtHjSZQuwYoqQo7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:36:40"} {"_id": "2sP62jq5cXaBFuNGA", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TdrRYfLM3AHuoK9NT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:36:14"} {"_id": "BWjdeX8C6Jdhpa9xC", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "paWWAKhFuM2dEepJ4", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:12:40"} {"_id": "NkRS7GxjhTxvr3inA", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vdwPCrScRCKyAJnZc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:13:28"} {"_id": "pTqgtQJ8ui9Tewu9B", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kHgBsNk3XRAsNccoN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:51:53"} {"_id": "ytjzvebLsLQnpMBzq", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^(adj + ~adj) )\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CsPbiZJrxAcvQb6C7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 10:33:27"} {"_id": "R43bJcmB38n3hBfim", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tsome adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SGYo7PebcuphJJ75a", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:00"} {"_id": "vvW4qSZQt7Ek3ApqP", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "MDd7HnFP8nTLPrPNP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:30:04"} {"_id": "HbEoZgnHLN4nn2WMo", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "5HdZtDhwh7TSPsQSR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 23:03:07"} {"_id": "cEkkWs55MBR5gcZBd", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n not iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nTqqRkwWZsDh8BrC3", "msg": "This expression failed to be typechecked line 31, column 5, filename=/tmp/alloy_heredoc12344461628834260485.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:58:18"} {"_id": "2o5B22RhTX9YCbD8K", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "WRh5dgajz8xyjZQnm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:25:54"} {"_id": "ybenavRB94onozjkp", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.adj~\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oercZGuHgQRDSbaTa", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:32:07"} {"_id": "bAvDq4vMTDdcwTgH2", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = no Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NMPohfgtSxE6Yf8s8", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:38:20"} {"_id": "6Q8CCYdcxrbKuxqz8", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aDD8qcJj9jbQZe2o5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:16:17"} {"_id": "vd6DBBmRi3zcQvv5w", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x,y : Node | x->y in Node implies y->x in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6NPn29JkaZkgC9y9j", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:53:05"} {"_id": "d7YZeBJegTmh5HxNf", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-23 15:40:32"} {"_id": "vdwPCrScRCKyAJnZc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tsome adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KDmRgxGs9Gq5uEjqr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:13:18"} {"_id": "za2fummCXS9skskD5", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-4-15 18:24:32"} {"_id": "aRvsj2MMR7DmkvSpR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QzTTF359irHeubEKL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:19:55"} {"_id": "aqdAaDe5pBwGkD8ue", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n *adj + *(~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "tvNTxceFyDFgcxypY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:23:32"} {"_id": "iuLH4J9zRgnGxm3kk", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node^.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tXMeAdtXeFkqipKdu", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:51:03"} {"_id": "dtyMydKR8wjRe6aEj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:13:55"} {"_id": "DE5BkQXerKFiFWFAt", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.^adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "sdoq7HzfJ26GksTRN", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:34:14"} {"_id": "tbtcKEzzux9JcZxYe", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cAEYaQQdzLb8xjmWz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:50:22"} {"_id": "tXMeAdtXeFkqipKdu", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GZfHst9nqJPvZ9Gyf", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:50:55"} {"_id": "YSMWRtm76RF6xCLRW", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n != n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ggn8uw9QnwYLq2rRm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:23:08"} {"_id": "bhrFZwoaWuGZv4MtR", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SXq9nd639PYBJj2nq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:41:21"} {"_id": "NQNv2FLszdBfecm2d", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HyZzkJAMZspCMchfc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:27"} {"_id": "mpxTjaQCfRaygXK4w", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n, n1 : Node | n->n1 in adj <=> n1->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CawnnXvb7SyY3PZJL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:12:20"} {"_id": "34Ge9bgKKjK82zZdZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n adj.~adj\tin iden\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GgqzDWP4dujBZf6C4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:08:20"} {"_id": "asrbgRx7gjCymt3gb", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RvtcEFRENBnkpDdMc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:08:38"} {"_id": "7QFjPrgig4PuFouAA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2kQE5trafm6kMmf2h", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 10:54:14"} {"_id": "aPqh9NetcAZ6WQu7E", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in id\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}\n\nrun {oriented} for 3 Node", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"id\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 18:52:42"} {"_id": "kcuJ9aj2gxpuHFMmR", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gTpjYjo3mYY5nn3St", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-4 16:35:08"} {"_id": "r5BW8YC3n43RjLeQ6", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ofALRJf4h9oygq7Qc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:22:05"} {"_id": "g5zfjn6fRkuFM8uc9", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uC3T3nTRdPm7CyP94", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:18:50"} {"_id": "CWhx6AedHW7zBpLFD", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y, z : Node | x->y in adj and z->y in adj implies y = z and z = x\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FBGhNW2BGujTwsgZF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:13:26"} {"_id": "9Qvcn5bK2gwDWcMAa", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.^adj & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mDT3r9m8hptQ3PiHd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:33:03"} {"_id": "hbq2DuAD6qzme9qiL", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t(Node . ~Node) in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:07:05"} {"_id": "DXfDB2uiZocLs58Eu", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P86Nvz6bvcN3ABvQy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:46:45"} {"_id": "kLKgqynmf2D5Yt3md", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "ZdJY8aB2xYbgMotfa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:11"} {"_id": "nqtxa9mWXnBCb9hnY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + ~(*adj).x \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "buXrhMdxYm84vkGGd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:06:00"} {"_id": "4LQRmWc2wc3BeMZy4", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "cvTe5vqm8QzhFD2GE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:39"} {"_id": "j9xfyw3hJQyZ6hpyn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj + ~adj.n + n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HQd862D763tBSiFwe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:56:41"} {"_id": "aSRJdc3xxJGRKbJv2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "4P5bRM8PADcpyPfAE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:41:58"} {"_id": "xgW3GJgedGDTjLEec", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\ta.^adj != a\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "g5zfjn6fRkuFM8uc9", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:25:15"} {"_id": "AAJmbvnQcpffYmiJW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Eo8BbHC5eLLsqz8BY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:55:25"} {"_id": "hjjgkPJQHht7nZpGb", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(*(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BnJN3MYs67Z3ggWi4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:04:17"} {"_id": "yPoqq6ErZvhi2GRB2", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "vDA5CYeJXSJdGMqMD", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:50:52"} {"_id": "Ln9eB7NSTRm2zF97K", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fMX3TdAR5kmQusfWD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:11:54"} {"_id": "rZDktbWsFujggPKnm", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj not in ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bbcDBwmcvxtvQb4CW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:17:59"} {"_id": "FGjDcdz3nPpiM8tBm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.*adj in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4iDSrcAPzSwL6uBG3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:51"} {"_id": "xziEyRJDKAqwcZos3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj & n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8AmBwStbPZ8zL4G5B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:48:50"} {"_id": "oP9CiSswcrkQK95xR", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj\n}\npred undirected1 {\n \tall n:Node | (n.adj in adj.n) \n\t\n}\n\npred undirected2 {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented1 {\n\tall n1,n2 :Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n\npred oriented2 {\n\tadj not in ~adj\n}\npred oriented3 {\n\tno (adj & ~adj)\n}\n\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n2 in n1.^adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\npred noLoops1 {\n\tall n1:Node | n1 not in n1.adj \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in Node.adj + adj.Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\u00b4\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}\n\n\ncheck {stonglyConnected } for 7", "derivationOf": "dAPKLnjtbfAqAQQDC", "msg": "Syntax error at the ? character. HEX: \\u3f)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:23:56"} {"_id": "v57GyoZoSAK2W9MQz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "DTCCwbewGKw7jF4rG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:28:37"} {"_id": "xxnXKcK4LbEAiG3Xk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "929LZEaH29LuwaywE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:00:12"} {"_id": "i3g8f7rNJBLq8epDq", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iuLH4J9zRgnGxm3kk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:51:13"} {"_id": "yyYTsuWnJ8zZNK8ng", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tlone Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8CCNqNw84dj3sktgQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-4 07:36:19"} {"_id": "wT6nn7RnYMALZePeX", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in ^adj.Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "Z2tHZptxjFkmCjcm6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:20:08"} {"_id": "icqXGmWKzDakAMGmd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ju7tRYQ7jvzhTsixB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:29:20"} {"_id": "5fLksqpXZ8aa3wth6", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HnphgZRakmZJYEjAT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:09:36"} {"_id": "oACDvFNXvAXmKwSgh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj.~adj in iden\n\t\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "RxQMr9oHxBGpgjq5S", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:14:05"} {"_id": "wSgrHbH8rTD6uw4Nn", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "5Nz7RXLggBXu3Eaqi", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:50:30"} {"_id": "MP3avBoYzg6s3Qb3N", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "JYH9Knp36mFjwWMHz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:36"} {"_id": "2X6FmbS57eZjwZMPz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some Node.adj or some Node.~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "A63Epaomb4dSL2TzW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:15:58"} {"_id": "DZkrgwsAsipzuQMWj", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in (n + n.adj) \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QQpsSGnBqcB8exdNR", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:28:15"} {"_id": "MQEzCTtRWxH9nAhjP", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Xwom6c7CHuxiqYtq8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 18:51:37"} {"_id": "oXYQYqiaeGrYatBub", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Gb6K3hq69PNcrHiuB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:12:48"} {"_id": "kJXkP2xRrDtRLdqXD", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 22:38:17"} {"_id": "dzxLNo52XtHchnAuX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tone Node or ( all n : Node | Node in n.^adj )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "PNW43uHJkjFDRiMXB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:59:57"} {"_id": "Yd6D5Csz5Y23A66Ck", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "Y3wLCTorZfBqwDY6a", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:07"} {"_id": "Z4yvcviJQZGr6R4uQ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t(adj & ~adj) in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BLcfk8q7BhnACYqk3", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:23:28"} {"_id": "5sTxGdm2fNSgrX8Cp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.^(adj + ~adj) || n1 in n2.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "HAW3hrJZJ7jZeKgtE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:05:49"} {"_id": "cNN54P3yFiLa9TwFN", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "ZJ5ycZtXhA6jiArJn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:40:54"} {"_id": "AvzmTY5XTiyoQSp4H", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "6JSoppwmCeNt95Fmn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:18:39"} {"_id": "ANBRQkMJBH2DYTaRG", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "bs4m5YMkh8sYE3NKP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:31:52"} {"_id": "oeBsQBjePAvm7XbKo", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall adj1, adj2 : Node | x->adj1 and x->adj2 implies adj1 = adj2\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "D7MdtgTBnwhnGFMJA", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:09:47"} {"_id": "gmfDPqoqFg3DLaDnP", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hLgPSxDba46S7wFEG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:40:11"} {"_id": "N87TtbjmeogFcagiW", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "6fnLbLGf2rhcDPD8v", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:53:42"} {"_id": "55QmwvEATxm3MFHxe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "N3kSKDQyeJrtoktMx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:29:01"} {"_id": "bfXFuAiREEWrZfzg3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8ednFzYj7MfrDppiG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:17:20"} {"_id": "FobFENpxQknxTpbGj", "cmd_c": true, "cmd_i": 2, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node - iden \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "s3x9FFkXFFxP3GvNX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:13"} {"_id": "eRWhutt7jsN9zFQPj", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yYPjy2jBkDdnoqpjT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 19:01:46"} {"_id": "jHqWwNDgfG99iF2nz", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.Node in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3yZRJAxM6XKEJFYwY", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:27:25"} {"_id": "pezi2p5oXDwvGAEk2", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ohkjRKcXm6tYj6smv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:20:54"} {"_id": "heqaNBmBoyrHGCsRb", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "F7zZMNCcyBQxa4FdN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:56:17"} {"_id": "E5uib7rCi8a3pmyXu", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.*(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EBdPh8DnGjcSQF5PB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:24:09"} {"_id": "5nMNja2nwj8iTxWtS", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node |no n.~adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6GM5o3oWPQm43e2kp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:30:17"} {"_id": "2qKHa3CPrD2W3QgJc", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a,b:Node | \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "s2Lkdpb22TcyXuw5D", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:43"} {"_id": "YFbhqrnJhu574qED4", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj = adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bXMM8HN32G8KRjyNG", "msg": "This expression failed to be typechecked line 21, column 3, filename=/tmp/alloy_heredoc803204136317058194.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:01:14"} {"_id": "gFXTLrLkAXn7KgbSp", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zvddRcbZ8QFYKDueg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:09:22"} {"_id": "Fvf7FC9TcjwmZxrTC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2 : Node | n1 in n2.^adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NMH5xSY6MKuYCK73A", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:33:09"} {"_id": "P4ZW9ixC47KY7Zue5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uN2ZqJwQTKh3Nw6Ez", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:08:28"} {"_id": "dXyMHkamAPhfWtgXh", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pSkSgnsNgsZz2xTYS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:49"} {"_id": "Q6RZR2udJBZSqKecJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(*adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "sJ582ExecG6La9FLr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:42:10"} {"_id": "pt5mfZtjWFyZ2qLjK", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not (a.adj=a) \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WHunptE7RoLYc2aYR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:28:35"} {"_id": "mcpiqLWwh7qSowzBn", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jCyvwGdQMJe4Mecxr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:53"} {"_id": "xLmjrmtTYAtHw3QJC", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n : Node | n.adj.adj in n.adj\n}", "derivationOf": "Xjji5QmJSvQ37mkcE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:30:00"} {"_id": "wcFBKZuZkJbnZ7SMn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8CPrawyt6Aiv2ktFM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:31:12"} {"_id": "xkCetzMSJxy3WvJ7r", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:20:52"} {"_id": "bNuHQNYWbJAwwkhh8", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "4xhE9D6Ccnmp4AtT5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:32"} {"_id": "BFuFqMDng6JXb5Sdq", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y z : Node | x->y in adj and z->y in adj implies y = z\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6Tiribo5vxyEhrWWi", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:12:05"} {"_id": "PrCWCPWQj68P96uTK", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YHSXicX4jb7EcvJHv", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-12 10:58:23"} {"_id": "CiABZADLDvYdgKLTr", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: None | n not in n.~adj.adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9LrsYQzSekg5PPB3A", "msg": "The name \"None\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:02:50"} {"_id": "HPP2kvFNYwfEBXrYv", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ui5CZSLTCEJxCsZb9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:26:48"} {"_id": "P4CHHp2SXTAkNYQgW", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall Node: a,b | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JzXgHvmpDBCgjEtxr", "msg": "There are 3 possible tokens that can appear here:\n, : =", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:13:02"} {"_id": "DtMn2H7krDJXyqnPD", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3t6AzYzvnzsMb9frF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:22:42"} {"_id": "63p4ookYqca7E6NtC", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZK9fXZxsdq37CohPM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:43:58"} {"_id": "ebxD7e4e9izvvSsLK", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1->n2) in adj implies (n2->n1) in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n1, n2 : Node | (n1->n2) in adj implies (n2->n1) not in adj \n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BtjAN6tGeqnp2YCM7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:36:08"} {"_id": "Ak9kEfZ4hKKEqXuEX", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj and n.adj in Node\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j7yZ7deQRuiNJhg5d", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:40:59"} {"_id": "3Gcj7eRAHLbTYywZ8", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tsome adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mjSqepcNqFaDCrF3b", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:25:14"} {"_id": "Jm7X8E5RvYecz6EdY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tone Node || all n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tone Node or ( all n : Node | Node in n.^adj )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "dzxLNo52XtHchnAuX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:00:07"} {"_id": "wnjExTkgM3WkG2Npe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n, x :Node | some n2:Node | n in (n2.^adj + ~(~adj).x)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oStHAHe58cP997aQm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:03:07"} {"_id": "8REsJyjRWqWPqeoh6", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tNode not in Node.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pPcgXFrMhPBaXkZ3g", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:49:32"} {"_id": "tsiY9ihcWckyThBgT", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | no n.adj in adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KSuk2Lqqh5BMZtvkC", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:12:46"} {"_id": "kqRsv6e8Sy4CrFiGY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | lone n & n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "72tEMMBhxCi3EY6Qu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:18:47"} {"_id": "RAoqZ2ut3CTCTXoNN", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n \n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:40:32"} {"_id": "dzJyQSGR5s5FQcEtd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(~adj +adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mwErw7ZWCMusvp6BG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:29:38"} {"_id": "zG7xmzrR6ysFKcm6o", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node, c:Node | (a->b in adj & b->c in adj) implies a->c in adj\n}", "derivationOf": "GgvnkhBkbu94gsmfr", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:36:42"} {"_id": "qhNEZeGFFEM4QTBrc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:50:13"} {"_id": "MeAE3nCMa6tzZZnvg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "tW3vyhDt5cF6jCjfn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:02:41"} {"_id": "u5tjoKwwW5KtCCdj5", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tnot adj + adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "izQ4YGqfxiPE2r7vd", "msg": "This expression failed to be typechecked line 14, column 4, filename=/tmp/alloy_heredoc3922764316627306042.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:26:45"} {"_id": "WBGiosGJ3KYhAiZJZ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EAzkeFhgrkaWmB6eX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:50"} {"_id": "p2oqHdqZkbam9J5mv", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n : Node | one n.adj & one n.(~adj)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4pjygyxeg4SWyTEcD", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:28:47"} {"_id": "qQBzKMLyMWJh5SXpa", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "h9T7DZqKkydk9qzBG", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:35:57"} {"_id": "ccwJei47u23WTaWAv", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | (n2 in n1.adj.adj) implies (n2 in n1.adj)\n}", "derivationOf": "6dhAEsunh2PpiuwuZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:48:25"} {"_id": "ehjdRJM4hGmm3SZGX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "XxPNhQKpnQjvNa3oe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:00:03"} {"_id": "FF87Eez2YcHfgWdZ4", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t^(adj + ~adj) = (Node -> Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "di7q7mjgyhN4PnQQp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:27:10"} {"_id": "bHKZE9tJgyrgAmjhk", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | n in n.~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zZpvttokcQPX6hjCF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 11:08:31"} {"_id": "Q9wkNLFMkwi9H2RYz", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1 ->n2) implies (n2 -> n1)\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9kJTtiAnkpFGXgSwy", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:28"} {"_id": "JzXgHvmpDBCgjEtxr", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall Node a,b | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "spX7bkf2bQr8i8QdS", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:12:55"} {"_id": "Yf2tyvoDSJN73LBmu", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Nzwys3E5K765ooFtx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:55:22"} {"_id": "iYnpMCyGqZzL7uxfB", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj + adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "u5tjoKwwW5KtCCdj5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:54"} {"_id": "8CPrawyt6Aiv2ktFM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZoxYhLYHYFrx5hmA4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:24:49"} {"_id": "eX7qbeN5LLPuvCp6m", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nno adj & iden\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pezi2p5oXDwvGAEk2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:21:24"} {"_id": "CbbjnxmTS5LAeZLMF", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n in n.\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uKuwxBdKrLQ6PXjTj", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 23:04:21"} {"_id": "uXwT7CQyaWYJhb9sM", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "diF9tWF7dcSb6CEYv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:42"} {"_id": "vmB7CurmsH88huLJC", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "zWHLSd4pYrrxsqFnr", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:04:48"} {"_id": "ka6aHwS5WggFiyXgm", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj = ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oFPcMykNmbnxEGL8T", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {PrimitiveBoolean}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-12 00:06:16"} {"_id": "tyYyEcdBna6HxtqZq", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj = adj.^adj\n}", "derivationOf": "cSkXjDatMtsbgnjdj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:03:22"} {"_id": "FBLvtAHE87pkJ4uHN", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GSeNSrXG2fYnMi9Ay", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:13:39"} {"_id": "am8446H83jupNWt7j", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2hX4dZ3WZ476jYh5T", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 02:16:24"} {"_id": "8LougFCAqGFh8jnHP", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | ^(x->y) in adj implies (y->x) not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NcJKfevQJhgWbKpqC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:19:16"} {"_id": "xWAz95PCxZhS5Zeqo", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n : Node | no n.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jEiyrfthxrLJcF5Er", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:54"} {"_id": "WHFcamPRhuNyTxNTs", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = no Node -> Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "udKjyhy9orThvhsR3", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:46:18"} {"_id": "WSkPtuZ8jtCSXFDPP", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in ^adj.n\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Tg9sBWSu2FavYjLsa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:43:57"} {"_id": "aA66PEm3eW6Cnddsd", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:36:15"} {"_id": "wQx8hFpRqbc3HJent", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "asrbgRx7gjCymt3gb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:11:50"} {"_id": "KwoukwPdoDrSeBtfK", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | some ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "ufcq4qkq5RMwfXZaS", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {PrimitiveBoolean}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:29:49"} {"_id": "eCGqgNzfHdzkYDMjE", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | n.adj or n.~adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "nhxssfvvPQdcGuuxG", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:12:37"} {"_id": "3Bg8TdnqmPaXE2tFk", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zbhYyBavRjYcW5LN3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:45:06"} {"_id": "oJwr3C2xD6eypc4sh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node.adj in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "gjPdWokZk8eoDykhd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:12:55"} {"_id": "8R2MnZcM2daPmbq2B", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yS2JfFqarEp5ZrkbQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:13:12"} {"_id": "cRkzAo3QGbK2zL58y", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.*adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZQfnABEnqL5BjocFS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:45:18"} {"_id": "9avngaBWLcTGqqsJZ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | n.adj = Node - {n} \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5Mt7JGSySzww92QEu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:45:30"} {"_id": "e46RYdrTHtCQZxuGP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + adj.x + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ysq6bLXeTeyspMCGQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:42:11"} {"_id": "TkRgMdLuAzQBTbM5Q", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1:Node | n1 not in adj.n1 \n\t \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1 in adj.n2\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "4YRsq9gyq9Zg4qwBB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:56:55"} {"_id": "o6TquqtPqJ4kgWxYs", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "a9PJLFq8sXcpcWvJi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 17:52:06"} {"_id": "iKJnnLr3TWeQaTtug", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2 : Node | n in n2.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Sa2cxPrzANrSRLqBo", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-9 22:59:42"} {"_id": "BnW433Ax97JfjDGwH", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "BMu3xkxwNacYF8GXE", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:32:20"} {"_id": "oEHtob9zjZggke79q", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | some n.*(adj + ~adj)\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wbt6Xnke2cWre4b8i", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:06:08"} {"_id": "PrfDQzeEarwzbvMxb", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n->adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vdi85Zbw6kXKGza5b", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:44:31"} {"_id": "fJYwKe2yYsXius76A", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^adj + b.^adj = a->b in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "powoNN5At2cNToaCr", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:48:13"} {"_id": "iyf6yeTFyham99vbj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n != n.adj\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-2 23:07:19"} {"_id": "zGakZwnPfMSoyxvgv", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n \nno adj & iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KwNcKLC2ya2T4WARx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:41:12"} {"_id": "LG4AMnJG2jBdxPpdX", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in *adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "c3bqRyz2ACP2BaBr7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:50:48"} {"_id": "QTqswobtcE75gzwYC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \tadj = Node -> Node \n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HAFmoKgKDjmhKAekB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:04"} {"_id": "G9oM82emj5bYFW3wa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:28:05"} {"_id": "anKqfNMJp9CyET2fn", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | (a->b in adj and b->c in adj) implies a->c in adj\n}", "derivationOf": "oCxh9QyppSrv6b3gx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 09:47:32"} {"_id": "K5Q3463NSLrRz6MMP", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n all a,b : Node | a in b.adj\n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JpHvjhebKNdpWMnK5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:09:42"} {"_id": "xKcGS9AnDJxfPZFJp", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fucryhfnSCHjPyt9q", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-7 19:54:43"} {"_id": "G9hbAn3yAdCxJXRNH", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dBwZS5CQy6Ycduk4h", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:34:22"} {"_id": "tSxZBcRMQTMgs99yB", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n in Node.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This cannot be a legal relational join where\nleft hand side is this/Node (type = {this/Node})\nright hand side is n (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-13 20:37:10"} {"_id": "RBWuxgYHS5F5n9dFS", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node = n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "LQcPBTEA8hAj8F4pt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:36:51"} {"_id": "fE24Yithtf3YqobJf", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n all n:Node | Node in n.(n->n.*adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "eyAfGvKE32ps5kyov", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:03:15"} {"_id": "yHqYBLWznWCADtRf8", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n^.(adj + ~adj) + n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3T73w2T322niJr2qH", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-2 10:32:05"} {"_id": "hqZc7CPeu2CYipTiN", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj not in ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w5AyM2Gy5Tovu2Cmq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-6-15 21:30:14"} {"_id": "5Nw9mFdi696ygvjD9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vnWPAcAsNZepj6BtZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:44:33"} {"_id": "9JZ9xyb6JNYYqYdHZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j6ssysdvTEXpuzDuA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:59:47"} {"_id": "zvZB5xQPSrHoT3pQn", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "f7WkgKppQLvkXyXkD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:13:36"} {"_id": "HKqBeGTGiftBKXtSS", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj =~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WzKL5ApSTw8xRbPgg", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {PrimitiveBoolean}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:25:35"} {"_id": "8dEpuEs54fv6SuWec", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies v1 = v2\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oeBsQBjePAvm7XbKo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:11:35"} {"_id": "wK7TQmhBWJy4aguSv", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | Node in (n.^adj + ^~adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aEo7rjgkWGZ8qRrJ7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:23"} {"_id": "gyAHma6CCS7tJx3Fh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:17:05"} {"_id": "YwqE29ipCpuymqjPx", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "rZDMuPRAzRaGbRSTa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 18:02:50"} {"_id": "fBBC4bydcgg2XEgoE", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:02:24"} {"_id": "cZDSxgB3RWLpvowza", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "FofspWqsiWAS2Jy6F", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:27:53"} {"_id": "eyS8GNH5uq2xanYhb", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "g2errPZgcF2Fw7pWm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:30:17"} {"_id": "X4gRNPjWA9B7M4rNJ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1.^n3 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "wCQGFjppqsFuq7hwv", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:59:30"} {"_id": "qMjgaYt67mxif8wHi", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + n.^~adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "8oJySioGsgkT2BgMP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:14:29"} {"_id": "SjHimjjmKqCLCPAHz", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) & (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "EYjijPu3nGu3HjNwa", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-16 03:39:31"} {"_id": "8ukpyhd7qmdzuC3Bv", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | no adj:>n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2gwGpcoMLLvAonzpL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:46:58"} {"_id": "D69NHhgXTn4XMA4Gu", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "5r2WS48gLsgbeQ8R7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:35:59"} {"_id": "xy8aKzRyYTHzucfGm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.adj.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "k9xbwYnAMTtS7LX3v", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:40:36"} {"_id": "cuR899z6BnXzsNSQf", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Xt3hfcTegHGDo3Aa5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:41:32"} {"_id": "HNuMXgkXgrH9Qwz38", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "rSid3s7chaWt6QJSJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:40:03"} {"_id": "EBdPh8DnGjcSQF5PB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.*(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WtGL7JAThmBDajHkP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:24:06"} {"_id": "6yLeXCu9pyDWgaw3y", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | x->y in adj implies y->x not in adj and Node in x.^adj + x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "6X4GfDd8G8jMYm6DA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:18:11"} {"_id": "TBWj2F3JDaJ49Nm3c", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj implies ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KGZLi3jguLdiNksCc", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:49:53"} {"_id": "foCFRGZzQz7pGe3wj", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall a, b : Node | a in b.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dowZHEnPPAahqaTTz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:22"} {"_id": "qfC7rEs4D4YJdKCZt", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "3uNA8nafpStupQyy4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:30:32"} {"_id": "3ZmTCB9kLgqJQc7FA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "o8CZ94XxLryNKywRX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:01:19"} {"_id": "S7HEvj6bXEYMkbZMd", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (~adj).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "YxkBiTpp3JHKtnnx5", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:48:36"} {"_id": "4fvczg7G9QHWs6JL9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EmrunfF22kmPsSiHo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:43"} {"_id": "ynHWP2X54StuuzL4W", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = ^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "K6oui934YNasa7TQs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:58:49"} {"_id": "96ob6vuBp8LLYns42", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "JQxRZsTfPSoCg5Ztb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:47:24"} {"_id": "eLnQye7Byy5Zd75CL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 15:29:59"} {"_id": "QN8KXLQh5iJ5yFHp6", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj implies no adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TBWj2F3JDaJ49Nm3c", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:50:01"} {"_id": "h6Y8bYLzcYBZrjXgX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj + n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "BqcDmRqNKdiD6d386", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:40:10"} {"_id": "eA4PrsWpPxHJexrZM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4NYb4RuGAon5szkHh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:00:20"} {"_id": "L4rafcZgLz66MbEmj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6Q8CCYdcxrbKuxqz8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:16:36"} {"_id": "tkfBh38zNMR6ErPQp", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "c4Jr3Pn4o2kzr4bKo", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:05:23"} {"_id": "vAPM7uHS5fMu2B9XR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ht36AzTmXNk9oqdeD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:55:24"} {"_id": "YkPEWPwPKkKRsjSaa", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XR7aKcxN3PSuPDZ2p", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:27:58"} {"_id": "yK7acPp9AMgiY2t8e", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | some Node.adj or some Node.~ad in adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "LksoNWBYn2wRp5GZE", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:17:34"} {"_id": "pHdCGb9Q4kWvYK8F7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "xkCetzMSJxy3WvJ7r", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:20:56"} {"_id": "qLtGL4cbpmEAwhP5n", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno ~adj + adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HZbAh7ykzzne6qkNR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:20"} {"_id": "o4hHApmqyEkBQPN3r", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "kWqt4eDoPN9rZXkcK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:17:22"} {"_id": "shpyipga6hkdoHSE9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7Pjck9mQNQQJXyq52", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-27 11:01:45"} {"_id": "FptBPAF4wQRWnHQHP", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n\n\n\n", "derivationOf": "euZFNEk79gotubk2Y", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 349.4140625, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-1-19 15:18:59"} {"_id": "vPmgNoFzZSsts7vBT", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "whD2BTo3zbGLEH5MB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:17:22"} {"_id": "w6uiHqoT3Pn5rhGjK", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MAcNBozp89qSFwRxf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:02:52"} {"_id": "kHgBsNk3XRAsNccoN", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zX4pnatEipZ4ffc3K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:50:21"} {"_id": "pPK5XWQHkKkjAjELd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rqt4MHCmidEb3dbad", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:46:55"} {"_id": "Ht36AzTmXNk9oqdeD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SbQJddTM766rWkL6Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:54:46"} {"_id": "JRM79kRj5wrJ7PvDo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "oACDvFNXvAXmKwSgh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:17:19"} {"_id": "YaMgbhrbZ9FfNxWds", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JpzeCcAXewj5g2Pgr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-7-8 01:58:52"} {"_id": "gr4C7yKCmpaCCK5LW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1->n2 in ^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pPK5XWQHkKkjAjELd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:47:06"} {"_id": "dNzW2ByAgGxdTEPNW", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ePw8nitbKKbB4F94h", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:30:07"} {"_id": "DHuhvp5s5CyhEx4F5", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y, z : Node | x->y in adj implies not y->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gYMAJRWxAW2vbJ56z", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:39:32"} {"_id": "Q9CLnEupXy7XCC6Kk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TQYzb79KL36HfXeTx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:05:34"} {"_id": "kRCwbhhpZHKXeKzQH", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zpTCjvjCbWxB7fq5x", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:43:14"} {"_id": "ybg47GHsB2iMmfrwS", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x<:^adj + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mgdrMvgjeKhmPWMtF", "msg": "+ can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 20:35:31"} {"_id": "QNc7as2cjg32YCRco", "cmd_c": true, "cmd_i": 3, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node - iden \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "FobFENpxQknxTpbGj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:16"} {"_id": "TQYzb79KL36HfXeTx", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | (x->y in adj) or (y->x in adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rgKwd6B7MTtqdhuKS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:02:31"} {"_id": "J6gp5Km8wrZo7MdMu", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj1 = adj2 implies that adj2=adj1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vrCdjth4BsX7DCiCy", "msg": "The name \"adj1\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:07:25"} {"_id": "JKYRmpS7ePy6D4zfB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | Node in x.*adj + y.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tY6vWuTtCTYKMHvrR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:56:18"} {"_id": "WgrWkS89Rm4orbYv7", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some (n1.^Node.n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "wSgrHbH8rTD6uw4Nn", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:51:53"} {"_id": "dcpYyj92Xk2xwuAfD", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \nall n : Node | Node - n in n.^adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \nall n : Node | Node - n in n.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8BHjuz4cYKwaQiMmP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:56:06"} {"_id": "HW36CsWuLpruSX4EG", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Fc9C4ZH9ByJjfgaHQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:10:50"} {"_id": "TAtwM3FEaryJSwmJ5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9EvJ3cHMCiTKBEW6u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:52:27"} {"_id": "Nm8SABkoMLXb8MBSS", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G4zqwMfokBPLALTn4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:20:21"} {"_id": "jiNuM9TFqPZ6xkr3H", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n:Node | n !in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n:Node | Node in n.^adj\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n !in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "z34s5ERmzfHEbmA7D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-6 20:53:33"} {"_id": "NtfQi9F65KuYyqXGr", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "eEQj6xGAuPE69H4Nr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:52"} {"_id": "fnHT9TTtHEhEGx34p", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tnot iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XpHdfv9QKwAzuxj6M", "msg": "This expression failed to be typechecked line 49, column 2, filename=/tmp/alloy_heredoc9824875621804726949.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:46:05"} {"_id": "dtEBNprChrYJpXnvH", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | a->a not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HMbgRtqd3ryfRMfd3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:38:47"} {"_id": "yS2JfFqarEp5ZrkbQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:12:57"} {"_id": "BMu3xkxwNacYF8GXE", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "S5pq7ZiYbGTMsmDqE", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:32:14"} {"_id": "8ZR9ooeEapN4Mon9W", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YkCCzKim7gJLQhfQD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:29:46"} {"_id": "d8epBJoPiNNBnypZz", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-6-10 07:20:56"} {"_id": "Jjh4pppDayqe4c44g", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node.adj | ~n in Node.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JGuQB2ub6zZskrc2x", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:08:38"} {"_id": "Mz88Q8cctjN3mGk8q", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.adj + adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "vFLnCjzBCF46ir4Gp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:27:33"} {"_id": "cL77F8QNj95tjuEBq", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n", "derivationOf": "7NxrvcYFdF7t5uvEC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 15:10:40"} {"_id": "ujT3HWaWkpBZBvX9B", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node = n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3Q3MX7mdNGrx5xq7u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:33"} {"_id": "DMgirw6w9y6JS2jsb", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pHCRtSNTnGPSNcymc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:28:43"} {"_id": "enQaDcNyd5wSFEg9F", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DxEdqk7h4k8THWXXn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:28:19"} {"_id": "Pik4BGKG99WwjhtBd", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KMwvNi8Lom7daQA6Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:32"} {"_id": "TJmP4Q4Ri5oAvekzK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "2f88wrQvrogKamQua", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:48"} {"_id": "Tg9sBWSu2FavYjLsa", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in ^adj\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "4oKWsm94d5qrhAdc4", "msg": "!in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-25 16:43:44"} {"_id": "45x8QFhZxeCwsLKxm", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in e1.*adj + c1.*~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"c1\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:44:15"} {"_id": "TfTyWDgvN3kuGctCe", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YiGtWYezEk2xTxC8R", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:12:40"} {"_id": "jCyvwGdQMJe4Mecxr", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QcRD5957JiXbxbX69", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:45"} {"_id": "CAH6AbzRogDRAJ8FP", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n not in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zgazum7dcuty6TcBn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:17:52"} {"_id": "bdxHpZXzakQnEJE9n", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tadj.adj in adj\n}", "derivationOf": "kxspMeeSdr48MN4z4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:50"} {"_id": "EwQCvoYcDrX2priKq", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Kj6ZJmcfDpBoi9YgQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:03:25"} {"_id": "w5AyM2Gy5Tovu2Cmq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-6-15 21:29:58"} {"_id": "WRh5dgajz8xyjZQnm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^adj + ^(~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "2LSYHQiLi3wRMbPPa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:24:30"} {"_id": "PWBHYLFaMRmcdNFu5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "AvcCQwQSuFCmrXh6E", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-21 10:32:56"} {"_id": "HALkfvTvfWNiWD25b", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "kgeKqCuZKoePpEeFP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:24"} {"_id": "z6CJqW89j8qLRuwbu", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n->n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eTT5yPyat3qaFt5qL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:18:54"} {"_id": "2FiETHvMeTuWvWoo5", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node - n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "t3q5xx68zxmmHzRgf", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 267.02083333333337, "y": 199.1999969482422}, "Node1": {"x": 534.0416666666666, "y": 199.1999969482422}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 18:09:48"} {"_id": "5EieyPXsbR8rCGAY2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.(~*adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sSadCegAWG2Szusu6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:17:41"} {"_id": "AtPtks487bZ2ykmbG", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a,b:Node | a->b in adj implies b->a not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "o47ouLtwZEW7bskG5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:11:51"} {"_id": "X67cZA6aocQJvrwRw", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n:Node | \n}", "derivationOf": "XapQvYWg2W3ovXP4T", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:33:07"} {"_id": "J25k33ShnBrvtX8Ah", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DFbuDesKhoJE8Eke3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:10:56"} {"_id": "vFLnCjzBCF46ir4Gp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.adj + adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Wq23upqnFa85q3kma", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:27:08"} {"_id": "NFgmCjiqhAwT2x3H2", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no adj.~adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "Rciy2qt6kyXSMuhfn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:38:00"} {"_id": "aw9q3AuFRz5EFLSSR", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^(x.adj) + ^(adj.x)) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fAexkNj8yrDiMJQG8", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:51:51"} {"_id": "AvcCQwQSuFCmrXh6E", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "NtfQi9F65KuYyqXGr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:54"} {"_id": "TJyyHd3byy9GLTj8R", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + e1.~*adj + *adj.e1 + ~*adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zsieAehvd5z7ctvxs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:51"} {"_id": "QCzrun7HDjtG3yMCk", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "HfXvNCbB8bvRYzrRd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:09:31"} {"_id": "4zGdc69JmS2d5g6oS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "sc99z6ooPwmmsPxQg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:21:09"} {"_id": "LDmbXxEWXgukq8WBX", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tone adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GK25gSiLt2BZN9zmc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:25:39"} {"_id": "F7zZMNCcyBQxa4FdN", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XSrtdPGcD94CurAMg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:53:51"} {"_id": "ogTBbTtwsGyheeaRz", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n: Node | (n.adj->adj.n) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FmPdNNChMgN5NxHgg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 08:58:21"} {"_id": "SEsN5pmfitwXTACP6", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yR9qScjw4yEABE9Z9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:36:14"} {"_id": "9wv2dFGTAsivD6aZJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a->b in adj and b->a in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "rSFtHpie6fzAoewfc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:00:59"} {"_id": "a5wTAXK7aC5GDA7wX", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xKcGS9AnDJxfPZFJp", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 534.0416666666666, "y": 132.79999796549478}, "Node1": {"x": 267.02083333333337, "y": 132.79999796549478}, "Node2": {"x": 400.53125, "y": 265.59999593098956}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-7 19:55:34"} {"_id": "w8sAfonm8fa7eHTgP", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & ~(a.^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZHgRB7HdX29c4Xicp", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:36"} {"_id": "wyyseoSPtcr384tnb", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Fvf7FC9TcjwmZxrTC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:35:25"} {"_id": "kgeKqCuZKoePpEeFP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "dWKqm4vFyqBWtWZ8E", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:16:59"} {"_id": "Bf2Dyx9ppecSdS9iu", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall n:Node |Node in n.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "EdNY8xKH5XtkfS8sw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:37:26"} {"_id": "KY7r5znHBPGQ9EgDG", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "B9FQ2Zay8vpuAEKGf", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:19:01"} {"_id": "zbhYyBavRjYcW5LN3", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZjvFk4CHyKXWjZKm2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:44:15"} {"_id": "bXpxKhtqY224iNTHM", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZeSnFu9qNN9d66exK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:15:59"} {"_id": "94k7j7T9tHG897EwT", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:34"} {"_id": "FYabHWaPYhcLHnY6A", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4fvczg7G9QHWs6JL9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:49"} {"_id": "FgDzhyF3aTXZggSF5", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "z5nwADSAhiS4NQ7sE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:47:43"} {"_id": "NJb2xfqcSe892zxLD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*adj).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "nH4sCaCw85cieSfzj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:39:35"} {"_id": "FfgxwQrEkoESssaSp", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj \n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "C4oN8bmpNmpXX6tBv", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:32:56"} {"_id": "qbrepD25Sb7i6BkdQ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n*.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fx3DPNGmAys3urmbo", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-2 10:32:19"} {"_id": "r7x9mJtJCyfHBbtrF", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj or one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "oJwr3C2xD6eypc4sh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 23:14:07"} {"_id": "eGERwi2E955ZpHmrF", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | n.*adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "CuushxHTdF63s7Emy", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 16:38:55"} {"_id": "FBGhNW2BGujTwsgZF", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y, z : Node | x->y in adj and z->y in adj implies y = z\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BFuFqMDng6JXb5Sdq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:13:15"} {"_id": "8zwjq3wXE6dMKJ6p2", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (some adj) and (Node = (n.^adj + n.^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (some adj) and (Node = (n.^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "SxYPjb2CDyKQdzXxZ", "msg": "The name \"n3\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:50:05"} {"_id": "D4wywhte7xWsWazSz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KXayan5TJWWb7muid", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:15:19"} {"_id": "GNfyFrmtT2a92hRCK", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | n.adj in Node\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DNWm3hqkbuyymMe7D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 16:29:47"} {"_id": "CS5vSsTLZuSnukQsc", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node-n in n.^adj-n\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Xwe97qC6hgX9vtfNK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 17:53:40"} {"_id": "ePw8nitbKKbB4F94h", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj + ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "83adEDau7DgBmRrB8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:29:56"} {"_id": "yi4q8osWt2Y7x24vw", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2HvLiy4Y5mk8vrTRA", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:41:20"} {"_id": "ud37uziuykypA5fbc", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kRCwbhhpZHKXeKzQH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:43:36"} {"_id": "3cwQLJm9mif64H74x", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kqRsv6e8Sy4CrFiGY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:22:17"} {"_id": "uFfxg4xfkm4psH25t", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HzgA5ju3QfGt6iXXX", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 444, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:54:44"} {"_id": "LyLXfXEtivMNSNNs5", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + adj.x + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "e46RYdrTHtCQZxuGP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:42:49"} {"_id": "HPCEBSNYXz4iwL9bF", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "aSRJdc3xxJGRKbJv2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:42:01"} {"_id": "ojC8JJk4nCfCYbLzx", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n \tall n : Node | n not in n.adj*\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Dh3L5RdJhPo3nCwKC", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:18:18"} {"_id": "3rd2rTwLDYGyfHp48", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n2 in n1.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AXnkcvMmvmvH3ZvkX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 23:27:09"} {"_id": "R2gtHjSZQuwYoqQo7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | no adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rmFwoeGAPJyg93TCZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:35:39"} {"_id": "paWWAKhFuM2dEepJ4", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:A Node | a -> b implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 3 possible tokens that can appear here:\n, { |", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:12:21"} {"_id": "GXzF9ZfxSbmbaZEX3", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n:Node | n !in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n:Node | Node in n.^adj\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "J9YLX4ooC69fp4xuL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:52:54"} {"_id": "LSzkFw2dZ34rpWtZu", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G9hbAn3yAdCxJXRNH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:35:15"} {"_id": "H3R3MBtFFZibw7ucw", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MxP2mXbkGLRJswuJQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:26:44"} {"_id": "LyDCCt7m9T8jtJFWq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n : Node | one n.adj & n.(~adj)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nZFuw9ijtZmK9zTbL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:27:47"} {"_id": "jju6tLNQ9gJyiiTn7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cfCbkr4w8nDTrFkmd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:08:50"} {"_id": "T8WeWwoJGoaciyHWi", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall disj n1, n2 : Node | n2 in n1.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YaYFgNxf5ydQ5f5tc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:50:05"} {"_id": "JHshE5CMinqsWFQH8", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~*adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8uRkKjAF5yhBHQAzn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:07:44"} {"_id": "zZpvttokcQPX6hjCF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "39aRNYiowhg2Go7sG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 11:08:11"} {"_id": "gTpjYjo3mYY5nn3St", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3YAC3ZvbGijJftPPn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:34:32"} {"_id": "kfsqxbkS5f5wSR3Xw", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6xQ74EXAhYb5eFr8j", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-12 19:30:47"} {"_id": "j7wgY9vGYXJYQukMA", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vTvkRQGn9fgHWwuLH", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:30:00"} {"_id": "wKv5Dageum5oCFvJz", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1 -> n2) in adj implies (n2->n1) in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n1, n2 : Node | (n1->n2) in adj implies ~(n2->n1) \n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jh2yRoLsdf3x4zRDN", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:34:29"} {"_id": "A4siLicMRu7wLjFSD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + (~adj).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aw9q3AuFRz5EFLSSR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:52:40"} {"_id": "cMhPkzDnwhEQGHPPr", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "B8WWL5CtD46jbDPa3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:53:03"} {"_id": "5r2WS48gLsgbeQ8R7", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "DKGcf8vwSjnwQZFJs", "msg": "* can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:35:50"} {"_id": "s5tGHdW5cHHN8ft4N", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n adj + ^adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hiqtu7BxZsQTpyiAg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:29:10"} {"_id": "6fnLbLGf2rhcDPD8v", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj in Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "oSZ7jDNvSRW9faPmL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 18:53:35"} {"_id": "3rBtg5JH8NqNPwZJh", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all ad : n.adj | #(n->ad.adj + ad.adj->n)=2\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wGqmFpvxwzFNSSzf2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 01:37:23"} {"_id": "bsieDb5fiRJc5amPW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\t some adj and Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "jyf9jpXt3fEWRv3QD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:12:11"} {"_id": "8a3WGNMxhGS9MBDFC", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n.^adj in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "dASZeA6BADRBxwJjq", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-6 02:33:18"} {"_id": "fv2gdbo7sqoaio7i6", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "q9QSfwuqcjHDSqLEQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:48:00"} {"_id": "TC4TEQrF4DhYb4Geo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + *~adj.n)\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vXWvjYDygKcYWG24L", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:53:25"} {"_id": "rHB6gonSnQxiTyns2", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1:Node | no n1.adj.n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sWDR9s3zwpeJxJ5ma", "msg": "This cannot be a legal relational join where\nleft hand side is n1 . (this/Node <: adj) (type = {this/Node})\nright hand side is n1 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-25 16:25:29"} {"_id": "MgQjhLst2BLDvnt2T", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kYjDqiFs3W65xPoeS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:34:12"} {"_id": "DqTit2jmAcspgXMdr", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n2 in n1.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1, n2, n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj\n}", "derivationOf": "3rd2rTwLDYGyfHp48", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 23:28:38"} {"_id": "oNHxcqHm5NbPSEz4z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + ^adj.x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 20:51:15"} {"_id": "EFTjANp3jDKA4ajyr", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = n.(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LMqrJsBfznRKFKDCM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:33:43"} {"_id": "bkvcJ4LARF3Py3hQH", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mXNHRCYhScZcv7FoM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:48:05"} {"_id": "xsQkzEwPPPNq7exCq", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x,y:Node | x->y in adj implies y->x in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *(adj + ~adj)\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3FnHLkAd2iMsa8Mua", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:10:27"} {"_id": "7KetZH8HjryX2Cn5w", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in(all n:Node |n.adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "buk8nppcfjDWyStow", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 12:19:56"} {"_id": "utCrxa6mqHJ8Kg97z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | (n1->n2 in adj) and (n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "eQo2woKMcZDg9JYZi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:03:19"} {"_id": "tmsLAQp4RrJeFndXy", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode.^adj in Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = Node -> Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n", "derivationOf": "a64AMhEEQPmDWjkZM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:08:39"} {"_id": "pSkSgnsNgsZz2xTYS", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:31"} {"_id": "uqL8QWjEsidXDawCD", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (~adj = adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ieirnAHTtuNhymNhT", "msg": "This expression failed to be typechecked line 21, column 2, filename=/tmp/alloy_heredoc8213187737038299853.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:55:22"} {"_id": "NJ3ahyNBdpiYyS72E", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.^(adj + ~adj + iden)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4qSTjaM5EBBbWdKQS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:25:53"} {"_id": "oWs75sxX7eo7JhfDb", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qaEvt5qs8SvX9d2Zj", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:28"} {"_id": "QpNoJewj39Qgufz4p", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | n in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.*adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P4iH3qEkPKrf24tco", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:01:58"} {"_id": "rzz6hXHAG9pqixcD2", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tadj.adj implies not adj = adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "u7bAiNcusxFDPixhP", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:22:52"} {"_id": "YAA66cb6b8h5twMeB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tcYAiwH4vZBNqaSX9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:36"} {"_id": "fmZqRrFB2QJfb7ubx", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MkfsJ5jMRhoJQuyzt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:49:31"} {"_id": "A59rXbc9NcBsh63JD", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "MP3avBoYzg6s3Qb3N", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:40"} {"_id": "hpFS5fcbXMecqkakp", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node, c:Node | a->b->c in adj implies a->c in adj\n}", "derivationOf": "bvhxNxEvLzp3X3NQ9", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:36:06"} {"_id": "PGREf5b8jLn5wF5La", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "JAKjA8EQMhziAtCCz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:57:14"} {"_id": "qbQBAMqapbS7XCQer", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj implies (no ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QN8KXLQh5iJ5yFHp6", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:50:12"} {"_id": "rmFwoeGAPJyg93TCZ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n.adj not in adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mX6NcFoGrkrJcW9EN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:27:40"} {"_id": "qFPFJFq82HSP59QGy", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "tyYyEcdBna6HxtqZq", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:33:52"} {"_id": "o4XqbD2GLKBcQxAEj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1 = v3 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rzz6hXHAG9pqixcD2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:10"} {"_id": "LFHegxZB5ZpkhDevB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pt5mfZtjWFyZ2qLjK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:29:00"} {"_id": "bgL4a7RyRonDDrLWr", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9ZS2uajtemKtkG7jF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:21:21"} {"_id": "G8D2c9cnobkghnioX", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pigaqdHEQKX4rwpme", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:31:39"} {"_id": "ajdnwWQxbxa34GE9s", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 01:17:58"} {"_id": "YcRvQ872FDyqcZqDa", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.(n.^adj + n.^~adj + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "LdWP2dDAsG4XG23Rz", "msg": "This cannot be a legal relational join where\nleft hand side is n (type = {this/Node})\nright hand side is n . ^ (this/Node <: adj) + n . ^ ~ (this/Node <: adj) + n (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 11:57:18"} {"_id": "zfNyz3XAcJEC7sMoJ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jcBxNEotP7SqDkLem", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:15:37"} {"_id": "MeFa8bC4mgjDXQQBu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Dv33MgmzRpB2JXhqg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:48"} {"_id": "S5spq8hq7vrNc29nq", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 implies n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "aDaWgWe9R3hqLBGbk", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:35:04"} {"_id": "QHsiCvbQSxFCHqSBm", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "44EhcGvAKc5ciZGvt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:29"} {"_id": "eacYrag4WRcH7ibgP", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t lone Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oafetzhayxbdDEhGR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:22:54"} {"_id": "nxtvAf8yXraoi2fke", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-11-5 10:55:27"} {"_id": "vGnjjxowm2atrQSwD", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WHFcamPRhuNyTxNTs", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:47:09"} {"_id": "Gb6K3hq69PNcrHiuB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(*adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HCJag2LRsbqmdP4XK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:06:56"} {"_id": "vx7ZtmK3CkDuFezNb", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in x.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:47:31"} {"_id": "KEygcLRqrq98v2H6R", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | some n2:Node | n1 in (n2.^adj + ~(~adj).x)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nuQDhXrF9MCmiiQaJ", "msg": "The name \"n1\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 21:02:51"} {"_id": "3YAC3ZvbGijJftPPn", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "x9eSTSnHXqABhod3C", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:33:01"} {"_id": "DTCCwbewGKw7jF4rG", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*adj).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "cZDSxgB3RWLpvowza", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:28:11"} {"_id": "NnD97FngaakznAD2x", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.(^adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "LtBCGBkJ4AYHrXWpw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:35:52"} {"_id": "ybWKKdJSYqFnAGd2e", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall disj x,y : Node | x in y.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T32GzoLs6mhmXAh8F", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:28:39"} {"_id": "6P8SZuavc34sx9Ado", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all a : n.adj | n in a.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ireSmZCH6CbEop5um", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:31:34"} {"_id": "JrhoinguxnPh3rBpt", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bNuHQNYWbJAwwkhh8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:34"} {"_id": "x4tP2DY6ad8BNErsr", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jKtw4yQThN57qtTyF", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-12 19:28:34"} {"_id": "Jk4J473bQDTs79MC4", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n Node in Node.^adj\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n Node in Node.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Hamfo3gTXyB3sQykc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:52:46"} {"_id": "BtjAN6tGeqnp2YCM7", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1.n2) in adj implies (n2.n1) in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n1, n2 : Node | (n1->n2) in adj implies (n2->n1) \n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wKv5Dageum5oCFvJz", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:35:34"} {"_id": "sFncjzQJ3bszrDEFe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + ^adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "2da6gvc3CmKm6SutH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:01:57"} {"_id": "gby4dnjG82o5vdASF", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:44"} {"_id": "XGAa5RaQNfqAqdoo9", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.^adj or Node in n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "6PneyhSLzx8DXNcmG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:22"} {"_id": "GK25gSiLt2BZN9zmc", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3Gcj7eRAHLbTYywZ8", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:25:22"} {"_id": "AD5iJBxhraqmtKqPX", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xabLPGXDa2FNci4R6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:28:36"} {"_id": "ut6b2YECbbZZ3uF2J", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eacYrag4WRcH7ibgP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:23:04"} {"_id": "iWpTFZwouTgzSxC2q", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tsome n : Node | no n.adj & adj.n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Xs6PXK5B7gm5EbWkj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:36:35"} {"_id": "QQpsSGnBqcB8exdNR", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in (n.adj+n) \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fFjvWNYLboWiA7m52", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:27:59"} {"_id": "ffHvbfZZ2mFgca4SY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n : Node | no (n.adj)\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vwQy2EBKajWBWsLYF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:28:07"} {"_id": "XQS7ZFA7omAwE2BuQ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 04:47:47"} {"_id": "56nkFLb9jb9etKncY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some n:Node | Node in (n.*adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "dAXPJoBt76PXdjmji", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:59:29"} {"_id": "5L7QrxcPTbnfS3pD7", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QRzXFMb8iYQRGCJ93", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:27:17"} {"_id": "EmrunfF22kmPsSiHo", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "e6gyXyfnXDijpSKrH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:14"} {"_id": "mc92eWCC5u2xu2e7m", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | some n.*adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "eGERwi2E955ZpHmrF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:39:03"} {"_id": "hJL5aXZdZdxRApTNW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n *(adj + ~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "xXQqP7CDJyJwvgpeh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:29:29"} {"_id": "T4L6RcW9Na3HPF695", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj^\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fAv7Xhia6YheCzuWf", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:51:34"} {"_id": "6Tiribo5vxyEhrWWi", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ncQcEZon9gFgfsg2X", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:05:56"} {"_id": "Rciy2qt6kyXSMuhfn", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no Node.~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "zJrx2RLx6XFpsb6yA", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:37:35"} {"_id": "NzcvWwu5ysdRR5n2Y", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tv1.adj = v2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mqn2xEuwT2t7gw2sS", "msg": "The name \"v1\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:12:20"} {"_id": "gkQACPvPKBt5h82dG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in n.^adj + n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "rcgyosQTwm55Ezaor", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:43:53"} {"_id": "5bgfCeRgSQNMyoT52", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n.adj not in adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sh7hpo9SfYjgwzitj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:25:19"} {"_id": "JHz6oG93BMwgzpHrF", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cRkzAo3QGbK2zL58y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:45:25"} {"_id": "ta8uNBfCEPhuCrxhk", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 592, "y": 132.66666666666666}, "Node1": {"x": 444, "y": 265.3333333333333}, "Node2": {"x": 296, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-31 13:48:04"} {"_id": "s2Lkdpb22TcyXuw5D", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a,b:Node | \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AtPtks487bZ2ykmbG", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:37"} {"_id": "6TEm8m9GsoESzEteT", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (+adj.n + ~adj.n) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WjT9HvSnLmBiWMi3y", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:19:55"} {"_id": "Y3wLCTorZfBqwDY6a", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "rThNcjfwwmTrMC3ew", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:05"} {"_id": "5gmqgMWKbEyBmpM24", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "pshafKoidADvxFtDM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:56:32"} {"_id": "dEmjXuubqBFpDrtCc", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "t6iHaESFGcGgm4YGJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:34"} {"_id": "4Yv3cbC4aGHeg2QpD", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n", "derivationOf": "HRPnsvM3is7KvwTWS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:07:34"} {"_id": "6x3oLrYxk63X6pZ5f", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BYz253ounAE6nRZR2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:39"} {"_id": "HY7ituoCXQpmhSTbR", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LPoxXseMHWRiFmAyN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:39:57"} {"_id": "3HYjT55Lq99LMurCC", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n.n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "gzvWRdMjenGgzmTDs", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:04:31"} {"_id": "R5TkrAtHvxK5MyWGG", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vAPM7uHS5fMu2B9XR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:55:37"} {"_id": "YpenAg9MZX4t7LcLo", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XtqFBu5NZygPvBY5d", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:22:57"} {"_id": "uKuwxBdKrLQ6PXjTj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cT3YdZRrxEZQCdxgj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:57:31"} {"_id": "Z2tHZptxjFkmCjcm6", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "KY7r5znHBPGQ9EgDG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:19:55"} {"_id": "KworHaSCqgMoJo9QE", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vPmgNoFzZSsts7vBT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:18:45"} {"_id": "ZoxYhLYHYFrx5hmA4", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5R98C8GC42ermSJ46", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:23:43"} {"_id": "CmPbQMPg4xWpGfT8u", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "NnD97FngaakznAD2x", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:36:36"} {"_id": "yzcYiZTmkvZ7z7zyn", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DmFdnf4uYaE2SHmoW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:25:53"} {"_id": "vrCdjth4BsX7DCiCy", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall adj1, adj2 | adj1 = adj2 implies that adj2=adj1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:07:17"} {"_id": "WgW3kqbYypLS8DeZq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CnZwTNRXcyFAmg8A6", "msg": "== is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 08:59:49"} {"_id": "2GPbPCksWsgdK2yuf", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aTFXxGraCaL56cwyN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:51:01"} {"_id": "634AjmmYQMvGD56bm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qAg3z5owryWxETJ2r", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:11:59"} {"_id": "Kjsji8md2wuRJRSc4", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.*adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T5LxcxvzFPgzM6ppv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 23:05:02"} {"_id": "eqzZSzBHkt5ivTpXK", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t(adj . ~adj) in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hbq2DuAD6qzme9qiL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:07:37"} {"_id": "i6Me2AgW2sM2zBrzR", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nz3LCC3iNsRbHuDa5", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:34:35"} {"_id": "Q5CrYbL4ZS94tg83v", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ~adj.adj in iden\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:15:30"} {"_id": "iyK8ErnhDSZ5AsstH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xrcAhpazxiK4Ho5SN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:10:21"} {"_id": "WDivSjAWZSjQj9kFj", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mcpiqLWwh7qSowzBn", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:26:19"} {"_id": "vs4i3u8EG3BG7YmsW", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YGsTthgtDdSYTcKLQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:17:06"} {"_id": "jZAEzzYqYB4Q3DBxf", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "52eDtwkrP8HxNQ2Hi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:05"} {"_id": "DztoFdw5sjsnMvrh5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all disj n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "NFgmCjiqhAwT2x3H2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:43:09"} {"_id": "BhnwarbHBnkj77Jef", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "u3iEef6ivSrfGyv5K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:27:58"} {"_id": "5CfuXq8oFubserfB7", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Q4mHSjyTj656wmBoc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-10 09:04:04"} {"_id": "dM65EZiR9cm32fceA", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "4patEsvmc5td87kJh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 11:11:00"} {"_id": "xrcAhpazxiK4Ho5SN", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : adj | ~n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2XjfsDcLEGp4RhwK3", "msg": "Analysis cannot be performed since it requires higher-order quantification that could not be skolemized.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:09:39"} {"_id": "t3q5xx68zxmmHzRgf", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node - n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "N8XbuXoXqHRc5XPSC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:09:28"} {"_id": "gipF97YGsCnTQLXHX", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pc5mBbjt8Trp9k3SN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:21:56"} {"_id": "AeiaTwwXMoYFEpFzT", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\tall e1 : Node | Node in e1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1 : Node | e1.adj.adj in e1.adj\n}", "derivationOf": "pF3jXH4KysW44Xmwm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:17"} {"_id": "jXjSkKzdMu5RdYPR3", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in n.^adj or Node in n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "cNN54P3yFiLa9TwFN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:41:59"} {"_id": "icTvGFwW9Jn5Caogb", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n: Node | n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "qbAqKPPfhnttXsrFQ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:08:47"} {"_id": "LzKrLcHDE5JSh2AZk", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1, n2, n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "LSzkFw2dZ34rpWtZu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:39:20"} {"_id": "qH6ddqBKCqvvHm7cm", "cmd_c": true, "cmd_i": 2, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}\n\nrun {oriented} for 3 Node", "derivationOf": "Jf6ZR7Ebjmgae6LFm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:52:59"} {"_id": "eYNSESfAcZzKkiyq6", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.+adj + +adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JDxTAWvLoA4TqHfWa", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:24:51"} {"_id": "cxbQWHBtNsqtGHHL8", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XDW5KJ7FPygeY3hqZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:15"} {"_id": "bXMM8HN32G8KRjyNG", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj = ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A2n2LKQ6Jg7qy34AX", "msg": "This expression failed to be typechecked line 21, column 3, filename=/tmp/alloy_heredoc5168884030703381624.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:00:56"} {"_id": "JsjoAGrv2g5wTxat2", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n: Node | n.adj.adj in n.adj\n \t\n}", "derivationOf": "gyTqsF6cx73CirwvE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:27"} {"_id": "rpDG3d3Q6nuNzARF9", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gSJ6PtQwxNcWKuDM3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:43:48"} {"_id": "yWNqsKawiZQAq2brX", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tall e1 | e1.*adj in e1.adj \n}", "derivationOf": "SoYveY2ns66b463wm", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:35:34"} {"_id": "C3bjgEbDrHssZvDex", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | ~(n->(n.adj))\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7gFr8dNmQtCP9NNKQ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:45:05"} {"_id": "6uYkyPjLoE8cZXSo5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fEsvvKKF3iXPAAjns", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:40:37"} {"_id": "dW3y3wsTDonM66dXs", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hqZc7CPeu2CYipTiN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-6-15 21:30:36"} {"_id": "9RxubbggiBWMxe9EY", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall disj n, n1 : Node | n->n1 in adj and n1->n in adj => n1 = n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "49ZFp4iMqv2eGczy6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:42:06"} {"_id": "HFzw8Qd8QHmj9qJrw", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \n \n \tall n:Node | some n.(n->(n.*adj + n.^~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "RbPtKzSxxzFhMdMYo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:05:55"} {"_id": "rjtQWe94aCSkZvFno", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n.adj != n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GQvF8Z9JoAeZi33zy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:32:28"} {"_id": "Ns6GxeNwMeJeu8oPH", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PGnREotvzzguDXnay", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:29:30"} {"_id": "zWHLSd4pYrrxsqFnr", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "3HYjT55Lq99LMurCC", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:04:39"} {"_id": "YyWyauYTtTm4GDrma", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "Ljz9qidxHYfgrr5mX", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:11:28"} {"_id": "J5CKsMMMdJ4c7ydRs", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FRQzokAiAztnzi79q", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:33:15"} {"_id": "HZfyhbrjsNWJo6mby", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "4LQRmWc2wc3BeMZy4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:41"} {"_id": "uC3T3nTRdPm7CyP94", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EAsGqsyYBuPMAiwHP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:18:22"} {"_id": "poJsJFzhs8Nrjbd5z", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "teutyHCcW47HNKYjN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:17"} {"_id": "xiipBcBE3cSQRgELp", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj != ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oKNyi3jGBjDFAnCkJ", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 22:00:16"} {"_id": "ufd7SdKBHcHPmxgPp", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "5q9xZCcQHzYs69tMz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:53:36"} {"_id": "74DtpnptG6TCyBeZ4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9Qvcn5bK2gwDWcMAa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:33:20"} {"_id": "QB4zzK5tuhkrhSNEi", "cmd_c": true, "cmd_i": 5, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "Mkod7Kkjvmh3rahr8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:34"} {"_id": "pfC4igj9xwMN7DmfC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WTeRu7Z8LA3ZrLXnq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:54:55"} {"_id": "vDSCWDH46cSoYvNeE", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qwYJZtweArAr2tdXo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 10:15:05"} {"_id": "iAX6Hqq6GKmY24CdL", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "faYnJkMG9tX3PMyqJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:33:59"} {"_id": "mvsDtLCSsxLD2xkdk", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "xjRj7RTXfqoh5QMEz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:18:03"} {"_id": "eyLDefH3KqqD5Yaz6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XgMtjkHeQT9YTkoM6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:16:17"} {"_id": "XJaahw7riQWBGFcbs", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in (n.^adj + ~adj\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CS5vSsTLZuSnukQsc", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 17:56:43"} {"_id": "buXrhMdxYm84vkGGd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n, x :Node | some n2:Node | n in (n2.*adj + ~(~adj).x)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wnjExTkgM3WkG2Npe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:03:14"} {"_id": "DmFdnf4uYaE2SHmoW", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YeXjYHXEh8ugePr7H", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:25:33"} {"_id": "QKQ3WHyYT2khuSMJt", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rRFXyk7NhR7ra9Z59", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:07:43"} {"_id": "T8tMb7MRzczEGdFcD", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HSYdSLgm8aSMH87TX", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-12 19:31:45"} {"_id": "stynskXSuZ3qvpREP", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | n->n.adj.adj.Node in adj\n\n}", "derivationOf": "cPnqreMEqv258Hqhz", "msg": "This cannot be a legal relational join where\nleft hand side is n . (this/Node <: adj) . (this/Node <: adj) (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:56:56"} {"_id": "RAZuv6tKSzqFkpybQ", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ojC8JJk4nCfCYbLzx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:18:40"} {"_id": "YZt46FwWbQY9EkbSa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:22"} {"_id": "6kAJwj478ZGxdXMbX", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n ~adj.adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 17:50:10"} {"_id": "dY8W9hca4YsLPEmoQ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some (x<:^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "76Me9R6wKKkBzJ8RK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:54:48"} {"_id": "rZDMuPRAzRaGbRSTa", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj = adj.^adj\n}", "derivationOf": "xWY2rGRM2euSXPSpr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:02:29"} {"_id": "vHnTj3G4Jp8sGSNWY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7TkTfM8p8ML6Li63B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:15:27"} {"_id": "KjuzvzgFetAznDKye", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tall disj n, n1 : Node | n1 in n.adj <=> n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "25kiopuRyFoeSCmvE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:14:36"} {"_id": "MLJDyfy83QAeqyeZn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "tRgmp4oPbQKfzZz8z", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:18:58"} {"_id": "8BHjuz4cYKwaQiMmP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \nall n : Node | Node - n in n.^adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n Node in Node.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jk4J473bQDTs79MC4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:53:18"} {"_id": "HbZQ7z4SDyWGXSKvq", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "jxETmstg586Ez7fZw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 11:17:14"} {"_id": "9whPK3AmwirNkCCNA", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some(n1->n2) and some(n2->n3)) implies (n1->n3)\n}", "derivationOf": "tkfBh38zNMR6ErPQp", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:06:06"} {"_id": "xBqhJzurZF5HQasH9", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pX3p9YASC7N6yDTr9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:29:04"} {"_id": "NpEP8K7JS8cFPKZ5L", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no ^adj.n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Fm7xWusqegp8HESC3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:33:25"} {"_id": "uGBozgPucQAsrAAFP", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\ta,b:Node | b in a.adj -> a in b.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mp5paAtwGLcTKjkhn", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:02:28"} {"_id": "PhFKeQ7Jt9ud8tE9o", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tNode->Node.adj.adj in adj\n\n}", "derivationOf": "KL9k6siqQpnbFtnft", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:04:53"} {"_id": "9QCuN5ycjqhNKxWnp", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in adj\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "X2oxyfPbQxoRTzgh9", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:33:24"} {"_id": "WX92g9i6ztzuWqX9Z", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dgJ5dgb3mofywz4sX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:47:52"} {"_id": "xe77X59H99QcRK5Tc", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | some Node.adj or some Node.~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "BgDPuEvqqTLgbpDQj", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:17:51"} {"_id": "RtxzR35rF6eCztgRP", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.^adj or Node in ^adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "aon4pP4mYF4x6HuaE", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:32:45"} {"_id": "fCHAuSfR8G55KL8me", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | x->y in adj implies y->x not in adj and Node in x.^adj + x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "92p7rpYXmdCjndDXB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 19:19:16"} {"_id": "jaWh8KA6Dun9iazQ8", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tone Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yyYTsuWnJ8zZNK8ng", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-4 07:36:41"} {"_id": "CkqGwk3jtzCKDNxXL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all a, b : Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MEP7NwKFuD2BBXnDg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:46:28"} {"_id": "X9EiLje9c6GhooJgH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node<:adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jyESQsmmG8gr8Gact", "msg": "Subset operator is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:30:46"} {"_id": "F4ZfekEfSX438668P", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Y6sBCTtMJfokmSBXi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:07:00"} {"_id": "GugpvZTKKMDbFP9Nd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + ^~adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cyTw2F9BHbyxdMiSW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:52:40"} {"_id": "cwBoxF3c3cJs8Z8xu", "cmd_c": true, "cmd_i": 1, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}\n\nrun {oriented} for 3 Node", "derivationOf": "qH6ddqBKCqvvHm7cm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:53:03"} {"_id": "69FSJ3oP6zJgxBExW", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "QCzrun7HDjtG3yMCk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 11:13:06"} {"_id": "EwxvrdFTunfheSAH9", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:48:40"} {"_id": "sc99z6ooPwmmsPxQg", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "p8s2Ndwdi2HQK2Yez", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:21:06"} {"_id": "6X4GfDd8G8jMYm6DA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | x->y in adj implies y->x not in adj and Node in x.^adj + x + ^adj.x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "FACfvxnynK2Wtjr9q", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:17:08"} {"_id": "JGuQB2ub6zZskrc2x", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1->n2 : Node.adj | n1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pxEcbYFmRGd48SpBX", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:08:16"} {"_id": "imacbbAbQ4Sw5fXE2", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.^adj = (Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2ivMGKDFS8P4iXz9W", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:11:53"} {"_id": "cSN9am85pguHERF95", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | b in a.^adj and b in ~a.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "3N4tWg44drai5ZCLt", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:02:38"} {"_id": "sMd9YFFxbdqrjFupf", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\n \t\n\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fcz5GEa6nWWo6Ts5C", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:15:12"} {"_id": "3MhCkaxWk9QiYQbgj", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n:Node | n !in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n:Node | Node in n.^adj\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n !in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jiNuM9TFqPZ6xkr3H", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "theme": {"currentFramePosition": {}, "currentState": 0, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 334.21875, "y": 199}, "Node1": {"x": 668.4375, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-12-6 20:54:24"} {"_id": "neaPEd2tfjnfAJtZx", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eDeq4PwotqfKhTubi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:09:06"} {"_id": "ZEJy254yg3BFjnXcp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jGR5o89Qh42dH3ZkE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:05:00"} {"_id": "zmQJaCGmHeFayAAEL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t^adj = (Node -> Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XZwpwX85z6f2Ytwzx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:16"} {"_id": "oaiY7tvxF4a7kBXDb", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\n \t\n\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \t\n\n \t\t\n\nNode in Node.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BtBek3yYrgX3EZi4R", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:15:27"} {"_id": "2RjswKKDwLvh8BnNF", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LDPkxy3yW4mdR79SG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:42:34"} {"_id": "ZaKGS7EQGoHEsvaN2", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n^adj + ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Za2xfEZq8Q7jjHTvR", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:52:07"} {"_id": "sewBk2hL4L8rmEpd4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj - x = Node - x \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZFicZu2Y7M6DT8b6J", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:36:00"} {"_id": "8dvDuvQcQi6ueFN58", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iyf6yeTFyham99vbj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-2 23:08:54"} {"_id": "fgjpS6JTFHpgpnnSE", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4C6KCkq7gtPYhcSJk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:19:45"} {"_id": "2n29Een8WGsMfpqZa", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.adj.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XqyCEnTeB8f3y9rcz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 23:01:19"} {"_id": "CnZwTNRXcyFAmg8A6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "== is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 08:59:43"} {"_id": "tGzussbXAWj37Bszf", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kfsqxbkS5f5wSR3Xw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-12 19:30:51"} {"_id": "irRXcj4mXFhmubfG5", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tnot in Node.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oH6DvoxZYyEDznAH8", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:57:05"} {"_id": "BSLJNCW8veoKKb84p", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj + n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "5dp4TH8nZ7YQfydAg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:41:36"} {"_id": "fKsMkPgb6YQwHT8fu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HPP2kvFNYwfEBXrYv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:27:35"} {"_id": "DKGcf8vwSjnwQZFJs", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "gyBaFJbzhzfanQpjn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:33:08"} {"_id": "CFEXupWgghvfe29j4", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some (n1.^adj.n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "WgrWkS89Rm4orbYv7", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:52:10"} {"_id": "4NYb4RuGAon5szkHh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iKJnnLr3TWeQaTtug", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:59:46"} {"_id": "km3sW3DrTRxZoNveP", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "tEA8ZZ769q2nP7NE6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:40"} {"_id": "83adEDau7DgBmRrB8", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:29:06"} {"_id": "74BhGT5chxBWvvLZ3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GqjAs5f6KYvitMn7T", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:27:42"} {"_id": "76k8myGtMxZTspEd5", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wgmJKxFqHxRNN2bpC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:02:26"} {"_id": "7oZabXtp8g32zRgpo", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "R43bJcmB38n3hBfim", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:37:09"} {"_id": "f59AgZSYopLWRxGrH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n in Node.adj or n in Node.^adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZypM2XgpdZzHqtqgr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:38:00"} {"_id": "mXNHRCYhScZcv7FoM", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DXfDB2uiZocLs58Eu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:47:39"} {"_id": "uQtgCbphsFAHGn6Ld", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^requires\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "neaPEd2tfjnfAJtZx", "msg": "The name \"requires\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:13:16"} {"_id": "3t6AzYzvnzsMb9frF", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:22:29"} {"_id": "5miBamw5phqP8TqXB", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KMwvNi8Lom7daQA6Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:32"} {"_id": "7yYY363aDtpbcZFgv", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "kfmijyopnSxnFzdmG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:51"} {"_id": "gsqYEoqEKhPhdTN2b", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gSkbpD2aCQXsZRG7f", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:55:53"} {"_id": "uv58BmvqFQyHuRhx3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "Fn3RwAWEEagpnnqTH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:35:58"} {"_id": "trtNKGkacjFShSFE5", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "DwfaAGREgW47K39G8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:21:16"} {"_id": "a64AMhEEQPmDWjkZM", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode.^adj in Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n", "derivationOf": "4Yv3cbC4aGHeg2QpD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:07:41"} {"_id": "HTX3LDQoCcmzwjAax", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.^adj + ^adj.e1) - e1 \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oXGjQ4YXhus8w5hLK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:25:38"} {"_id": "25kiopuRyFoeSCmvE", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tall disj n, n1 : Node | n1 in n.adj && n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LboWQx9RPw9C3TrRi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:14:27"} {"_id": "vDDKTrQsrTwnRjwAY", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some (x.^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iqshFoJ3RqsLXXjid", "msg": "This cannot be a legal relational join where\nleft hand side is x . ^ (this/Node <: adj) (type = {this/Node})\nright hand side is y (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:54:07"} {"_id": "ShDfQyxvFTQ3tdwSJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ng5PBvy4P3Wah4B7f", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:33:17"} {"_id": "zEWZC32rgdonuMxko", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj + n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xziEyRJDKAqwcZos3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:48:56"} {"_id": "GWzJaCnL7DZmq3KND", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WgBRZ6sStaqR2Hv7J", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:19:27"} {"_id": "3oY9XM2EdKkEdNivt", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | no a^adj=a\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MiBJFQMcroETWrYfE", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:21:56"} {"_id": "RLAGpubJ7CM44o9PJ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj = ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "q5ntwvfskcZmAoiX5", "msg": "This expression failed to be typechecked line 21, column 2, filename=/tmp/alloy_heredoc727937981028370719.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-3 09:18:32"} {"_id": "Q4mHSjyTj656wmBoc", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G9iHtZCTosD5nNZTp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-9 22:23:36"} {"_id": "bkm9Qi6wySs59LNxB", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:09:05"} {"_id": "JkRGeH5JR7hjubT4r", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | n.adj.(~adj) = n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YFbhqrnJhu574qED4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:04:35"} {"_id": "p9dmJysCpfRCg5TaP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.*adj )\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "XMgX7CbdJzQnY84qK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:26:39"} {"_id": "pg83SuyYBABmYuQeo", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "MxajR47d4JR7f9tJh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:36"} {"_id": "Dv33MgmzRpB2JXhqg", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KNMD3RSXrkEopafo6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:46"} {"_id": "c5uxYBLzL7tPdfoZm", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GTR5sTBzz6gyv3Ku7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:09:26"} {"_id": "pKCyjNiZBmbcCbrDE", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj implies a->not a\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RxG6q6qfMs5X9shvx", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:38:14"} {"_id": "TENr5jM2GSSX49ExJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | (Node - e1) in (e1.^adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pB28tDFuQa6987vrv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:32"} {"_id": "XGD9Hc8iifRRMMNoz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "am8446H83jupNWt7j", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 02:50:30"} {"_id": "fDJvS3Se98ebRAZFZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:48:37"} {"_id": "mp5paAtwGLcTKjkhn", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\ta,b:Node | b in a.adj implies a in b.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:02:01"} {"_id": "qgZXYzStzPzwqBBaY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1, e2 : Node | e2 in e1.*adj + *adj.e1 \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jRryt5ZmRaGGk63cD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:22:44"} {"_id": "Nzwys3E5K765ooFtx", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hnKJvuirvyZHeZeLs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:55:14"} {"_id": "kRcXZck5gHaRWrQkn", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in (n.^adj + ~adj)\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XJaahw7riQWBGFcbs", "msg": "+ can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 17:56:51"} {"_id": "GZfHst9nqJPvZ9Gyf", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno *.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YkPyGD29f4sHMaueX", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:50:46"} {"_id": "hHnevD2LDhipiXwBJ", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "grgXKknv8TJMDYX7W", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:59:20"} {"_id": "fAX6ecdeNRcyjZdJu", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.(^adj + ~adj) + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | (n1->n2 in adj) and (n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-19 10:44:39"} {"_id": "YhkotaN8waKTT3cDi", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies no (y->x in adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GZQwdTcqqamdhJDzB", "msg": "This expression failed to be typechecked line 21, column 41, filename=/tmp/alloy_heredoc7097643054256368207.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 17:52:59"} {"_id": "7oSSmnDYCFLybjHtb", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BowpShFuG24JadnrB", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:20:08"} {"_id": "vQuftdrL93TQLrAQt", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj + iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wf8ybW4cG8L5f4RDd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:23:24"} {"_id": "9x7K3rrq9QApat6GW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + adj.x + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LyLXfXEtivMNSNNs5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:42:53"} {"_id": "P86Nvz6bvcN3ABvQy", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tifQRriK8AisDwynD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:46:16"} {"_id": "mWSd4yhDW8BXgwsLa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall x, y : Node | x->y in adj implies y->x in adj}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3NRpaL8Cjh8SdocZk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 11:14:09"} {"_id": "9EvJ3cHMCiTKBEW6u", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj & ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KyHJiQtwSF6nTGPXE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:52:20"} {"_id": "T5LxcxvzFPgzM6ppv", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8nQJAsGJKN4m66qhx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 23:04:38"} {"_id": "zvFCL8JLxYfQGDLEt", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node = (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ba7yDTkS3TxH3uY5D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:32:52"} {"_id": "rFQPzb23E9idiGsSd", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj <=> n1 = n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7LAkLrzAxuxqJsNHQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:41:48"} {"_id": "ozrwf9q78A8MvfBBh", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj implies not (v2->v1 in adj and v2->v2 in adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KaDCBCXwAskT5Jj6W", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:41"} {"_id": "x9eSTSnHXqABhod3C", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yzqzey5Jt2SBL9snj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:32:30"} {"_id": "dGZBfBeAML4qLh2q9", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tNode.^adj in adj\n}", "derivationOf": "LCGomNRQLJc92jw38", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:33"} {"_id": "h9JbLnCXDK4kwWqXF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in Node.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "5gmqgMWKbEyBmpM24", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:56:52"} {"_id": "gusmsvuZH7dSvqWN4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "u6Nybtof7zbcX57vj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:09:35"} {"_id": "rcxayqub3QAXLZLyP", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nno adj & iden\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hzWpr4tZ3uLZ8dgKz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:19:12"} {"_id": "37zxAFgSSWBXCrZrx", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-2 18:19:39"} {"_id": "5YcrfC6q9z3ioZrpK", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ec76DSfY3CScDBozx", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:25:59"} {"_id": "XqyCEnTeB8f3y9rcz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eA4PrsWpPxHJexrZM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 23:01:02"} {"_id": "FeLy56GvHkr3N3LLM", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tadj not in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dW3y3wsTDonM66dXs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-6-15 21:31:03"} {"_id": "hi3qwPHemQy9viuvr", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\ta not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xgW3GJgedGDTjLEec", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:01"} {"_id": "CyXGWzhdSmuNQCGuD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n).*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5ukA2Z4mHcsR79Gvk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 11:33:13"} {"_id": "SNv6qSJHXTFFgYgs9", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2RjswKKDwLvh8BnNF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:47:29"} {"_id": "9d4CR9rNLH4ihev7g", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xbZ9ZDX7iB7s7d3aY", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:24:21"} {"_id": "gcoHN2n6KxBqD6bP5", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno v.~adj + v\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qLtGL4cbpmEAwhP5n", "msg": "The name \"v\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:35:43"} {"_id": "oStHAHe58cP997aQm", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | some n2:Node | n in (n2.^adj + ~(~adj).x)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KEygcLRqrq98v2H6R", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 21:02:57"} {"_id": "uQmSas6FoysfT5SLY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n : Node | one n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "83GZ2K4kpEha8pME2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:27:07"} {"_id": "hcXdMbWyXLkfzMftc", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | some n.(n->n.*adj)\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "pqTmZ9G7CZDrcbdsF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:39:30"} {"_id": "QzTTF359irHeubEKL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fgjpS6JTFHpgpnnSE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:19:49"} {"_id": "9ZS2uajtemKtkG7jF", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Nm8SABkoMLXb8MBSS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:20:52"} {"_id": "hLgPSxDba46S7wFEG", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "emDWrWp3hivTdGnSo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:40:04"} {"_id": "iwzaD4guRZNCYqrsN", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\n all n:Node| Node in (adj.n + n.adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "SJX6fhnBga25wNmmc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 12:48:36"} {"_id": "BtBek3yYrgX3EZi4R", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\n \t\n\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \t\n\nall n : Node | Node in n.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sMd9YFFxbdqrjFupf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:15:22"} {"_id": "asMF7qME7YJkCkKhL", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sAdzQFJSAMc5Rt4Wu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-2 23:17:59"} {"_id": "FbFzdbLaHfHkmkEMn", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "uunNuEbgmMX9nef5v", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:33:02"} {"_id": "vnWPAcAsNZepj6BtZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "R3fzT34Eabz4aCBbj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:43:45"} {"_id": "4C6KCkq7gtPYhcSJk", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rcxayqub3QAXLZLyP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:19:22"} {"_id": "4YRsq9gyq9Zg4qwBB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1:Node | n1 not in adj.n1 \n\t \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | n in adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "fHaJtr8wLsawDD7Fe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:55:13"} {"_id": "fPuvpXeHrR8oT2txM", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cMhPkzDnwhEQGHPPr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:53:40"} {"_id": "wpx4upTZmPmNrR7yK", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.^adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "kD2QxxHqb9RjTn8cJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:53:13"} {"_id": "Gfe7t4qqsT9ptRDTk", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PBYSJ6SASYLhcf5rE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:29:31"} {"_id": "jB24y2DoR8k9ZKqjE", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^(adj + ~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "pDmm4d3nCk3Yug3Xv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:28:29"} {"_id": "N6RTGkTTDZGAPSRo2", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:07:09"} {"_id": "z34s5ERmzfHEbmA7D", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n:Node | n !in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n:Node | Node in n.^adj\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n !in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GXzF9ZfxSbmbaZEX3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:53:25"} {"_id": "zPqFCqDqN8amgcZgo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + ^adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "LyrP3iLXNNzAy34nQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:07:58"} {"_id": "v7x3XZ9RkQnhu9YE3", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MM5KnTqBWE87ALdR7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:31:24"} {"_id": "Si9acfc3RebpHv8F5", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no Node.adj & adj.Node \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\tall e1 : Node | Node in e1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\tall e1 : Node | Node in e1.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1 : Node | e1.adj.adj in e1.adj\n}", "derivationOf": "tdz9n8y2AubWDxsho", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:57"} {"_id": "u3iEef6ivSrfGyv5K", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5fLksqpXZ8aa3wth6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:09:40"} {"_id": "ndTXiSNNL5aDcbsr6", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nall n : Node | n in n.adj.~adj\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mWSd4yhDW8BXgwsLa", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-14 11:14:17"} {"_id": "5Z8yNRmJMuePYQNsi", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2:Node | n2 in n1.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1, n2:Node | n2 in n1.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1, n2, n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "joGs3DnJRbyuDYg9g", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:40:57"} {"_id": "GB87Bxscg7DENFuYT", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some ((n1->^adj).n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "rQCt8axSmXekCzjwT", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:53:34"} {"_id": "rpi2PDg8xa795Nywy", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a,b:Node | a.^adj + b.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZvHxDKndqbLsnu2sL", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:46:55"} {"_id": "YbbjjZFEnQKtHXxta", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj*\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T4L6RcW9Na3HPF695", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:53:03"} {"_id": "LDPkxy3yW4mdR79SG", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bhrFZwoaWuGZv4MtR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:42:28"} {"_id": "Jh2yRoLsdf3x4zRDN", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1 -> n2) in adj implies (n2->n1) in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "guDRNzizevj6BSTgD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:33:26"} {"_id": "oiDoWRapoErxrbBkG", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.(^adj.y) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jpPcbP7Fdep4SRLQQ", "msg": "This cannot be a legal relational join where\nleft hand side is x (type = {this/Node})\nright hand side is ^ (this/Node <: adj) . y (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:12:47"} {"_id": "PWQCB5johBc2g8TxQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node - n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "nwHa9hDtsY5ry9mog", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:08:29"} {"_id": "qprTRhnpbBwTbLHcr", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.^(adj + ~adj)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JE2ZD87KjZiwc8Ypz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:22:56"} {"_id": "nRYTqBShetajwFeH6", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\ta.^adj in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eRL96wYnL6KqzRkgW", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:01:16"} {"_id": "9aYhTs3pGkZX2r5Lx", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aA66PEm3eW6Cnddsd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:36:47"} {"_id": "LksoNWBYn2wRp5GZE", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | n.adj in (some Node.adj or some Node.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "ZGmoBAzeHgGTa7MN8", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:17:04"} {"_id": "DMkFA5zkzKsfQZGnH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n : Node | n in n.adj.~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XF4RQJhpSmrbdL2vX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:05:10"} {"_id": "CHzj7xdj3YA9itKex", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | ^adj.n = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8tanQHhqfQDxaago9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:19:34"} {"_id": "nz3LCC3iNsRbHuDa5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj and not a->a in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xdkvYFGMPQf5MyfFW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:33:01"} {"_id": "h2opqd2XmxF98phTb", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tnot Node.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "e2cC3t9dwbriQ4kti", "msg": "This expression failed to be typechecked line 49, column 4, filename=/tmp/alloy_heredoc7862548451349168640.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:44:39"} {"_id": "kg3CmxMSRBSCJq7Sd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \nall disj x,y : Node | x in y.^adj\n\n\n\n\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BAdEsqgpkhPEAvYwZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-3 07:37:12"} {"_id": "bs4m5YMkh8sYE3NKP", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj \n}", "derivationOf": "dGZBfBeAML4qLh2q9", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:46"} {"_id": "cT3YdZRrxEZQCdxgj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n in n.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nsNzFJ8KCF8KBHoYT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:57:25"} {"_id": "qFA8fmf3C7m65AuQr", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "J25k33ShnBrvtX8Ah", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:15:16"} {"_id": "3T73w2T322niJr2qH", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+n^).(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8hY9ca88DXqdfkoQo", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-2 10:31:52"} {"_id": "uunNuEbgmMX9nef5v", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "AcD8ckn3FwJ9QKj39", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:32:02"} {"_id": "39aRNYiowhg2Go7sG", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dFoxxa4cvsAjoq6bc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:53:37"} {"_id": "WcHG5rPwRm793sFiP", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & -adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oWs75sxX7eo7JhfDb", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:17:35"} {"_id": "6xQ74EXAhYb5eFr8j", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "x4tP2DY6ad8BNErsr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-12 19:30:35"} {"_id": "fcz5GEa6nWWo6Ts5C", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\nNode in Node.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NddK5fbwd7yzcbb2y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:15:04"} {"_id": "8XQSdXgRSvhihY3mw", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in ~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vxmFvR6rGwasrQHqm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:57:22"} {"_id": "oJShrDP5qiBm3WQ7e", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n != n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qsuKgTPwMBLsrK6Lj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:14:40"} {"_id": "ni4YmaoJ7ebXuubkw", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "n8dJhmQDNT7hgAtC3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 04:58:03"} {"_id": "5bXgbwPKiFWAk4Gso", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GQe9KoQzMBshB5drx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 21:28:27"} {"_id": "vZA56bT7MZKudfiKp", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node.^adj + Node.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "p5x2pAWAge8ieP6J2", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:58:01"} {"_id": "onGQr4M9P84XGEXEC", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Dssd4gqvbnWTXwMnw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:10:51"} {"_id": "G3AW2pd2jkAx3Cusp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 14:45:38"} {"_id": "xSzfhWXdkfytyqWfe", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "FfCAwNKTfMAnBAmf6", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:49:56"} {"_id": "DXLvwzGzLQyv3JQsR", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oBW9mZSxHC5d4p4L7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:37:16"} {"_id": "Eie9KfMXo46vsRHZd", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "nLStFi4vux6DTYsQ3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:39:04"} {"_id": "5pFowB8Liqryj2Mme", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj & ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wn7QpJo3GET8sTavR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:50:02"} {"_id": "FhkQdwvv3SyEQeSkM", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj = null\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eFHKYCFYoj5DbffBw", "msg": "The name \"null\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:05:34"} {"_id": "oCxh9QyppSrv6b3gx", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b->c in adj implies a->c in adj\n}", "derivationOf": "QFsobGWiAxKdapatQ", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:46:53"} {"_id": "q5ntwvfskcZmAoiX5", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj = ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "37zxAFgSSWBXCrZrx", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {PrimitiveBoolean}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-3 09:17:48"} {"_id": "bQZZt2ffBNzTZzk5C", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tone adj & one ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LDmbXxEWXgukq8WBX", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:25:59"} {"_id": "vGJXLqysWoNMNtctu", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QPYiym6jdDhuGf9ww", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:38:05"} {"_id": "7w83DHLHtdzjhfWGJ", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n: Node | n.adj.adj in n.adj\n \t\n}", "derivationOf": "M7XY4kfco6JHjx5hC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:53"} {"_id": "BowpShFuG24JadnrB", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hgYHQfLso9zNmZ5ft", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:16"} {"_id": "JmkP3nGZoNgzGMHCy", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-13 17:07:37"} {"_id": "e6gyXyfnXDijpSKrH", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj = adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cikJhLAbNk3nZ6qiy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:46"} {"_id": "FKCf2nDBZE5qDX6Tz", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all n : Node | some adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wAykBk3paE8MwEWG2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:27:26"} {"_id": "pF3jXH4KysW44Xmwm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\tall e1 : Node | Node in e1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YAA66cb6b8h5twMeB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:58"} {"_id": "cfCbkr4w8nDTrFkmd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.^adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7pxdwusxoz7FoP5ak", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:08:34"} {"_id": "GQe9KoQzMBshB5drx", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MirTmyX4KtMiqDxLS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:27:32"} {"_id": "Xqv8zkd8g24ZDtFzc", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "RBWuxgYHS5F5n9dFS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:38:50"} {"_id": "rgKwd6B7MTtqdhuKS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x->y in adj or y->x in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5AxeaH7bk4Rd745mL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:01:51"} {"_id": "Eft3Q6BZ6aEjQ3tPJ", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not int a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3oY9XM2EdKkEdNivt", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:16"} {"_id": "dgxo3wxvvXmezFX4X", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*~adj).x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oXYQYqiaeGrYatBub", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:17:15"} {"_id": "TBdaJZsFWnJKy6awm", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nall x,y : Node | x->y in adj implies y->x in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "y8MeLPSDgxYnydeLJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:42:51"} {"_id": "PBYSJ6SASYLhcf5rE", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DMgirw6w9y6JS2jsb", "msg": "There are 3 possible tokens that can appear here:\n, { |", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:29:24"} {"_id": "3R4FWoEx2AfM8j8Kt", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | lone adj.n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jHqWwNDgfG99iF2nz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:11"} {"_id": "n4rToR6dp8e9zMcAG", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "G7dxsqa5FybTy3N4h", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:53"} {"_id": "FsdCeYSB6oWCNqhWJ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t~adj != adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NrJdrZRe4QZb45QN6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 14:48:03"} {"_id": "ZEksX3b8edBWimwBn", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1, e2, e3 : Node | (e1 -> e2 in adj and e2 -> e3 in adj) implies e1 -> e2 in adj\n}", "derivationOf": "HAnaxx4EM5eht5CJC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:32:59"} {"_id": "grbFe4YDzaekwkHxW", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n->n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gMPY6CRYXvKCwi8bo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:03:42"} {"_id": "WTeRu7Z8LA3ZrLXnq", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZzpymFCCXzKY2h4Fj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:54:43"} {"_id": "f8jQfWnC5p2au95cf", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t(Node -> Node - iden) in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t(adj . adj) in adj\n}", "derivationOf": "hmbJwAto3LtSYod5d", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:29:58"} {"_id": "38bD9AmmEwn5p4Dfd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gsqYEoqEKhPhdTN2b", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:56:06"} {"_id": "6dshFZEpbYAJhmj2j", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "mG6LXsvtRcfqivNjK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:54"} {"_id": "hTLNqwnhyodDB9Pvh", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode.adj = ~adj.Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:59:33"} {"_id": "HSYdSLgm8aSMH87TX", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fe8CKvsgqixD69uKc", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-12 19:31:34"} {"_id": "EjRkx6a4aP372tqzs", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RfzYheypgR2R2E6GG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 22:41:10"} {"_id": "rRFXyk7NhR7ra9Z59", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kszYZvCNBHmZNwECP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:07:10"} {"_id": "sJ582ExecG6La9FLr", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(*adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "NJb2xfqcSe892zxLD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:40:17"} {"_id": "XpHdfv9QKwAzuxj6M", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a : Node | a -> a not in adj \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aiJp8RfrXNxCuNsX6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:44:10"} {"_id": "MrLh5PEEiGwq2eCau", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "DJfn2bPHZ27XxPRkd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:47:20"} {"_id": "rqt4MHCmidEb3dbad", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | n in Node.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6fcusjn5E8xXG5WBD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:46:33"} {"_id": "SxYPjb2CDyKQdzXxZ", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (some adj) & (Node = (n.^adj + n.^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (some adj) & (Node = (n.^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "tz9aPBRES7goqF5Qg", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:49:57"} {"_id": "SJX6fhnBga25wNmmc", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t Node in Node.adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "HoErSgZybWu3QBQpn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 12:45:47"} {"_id": "P8kjmvS5xcP2jFgv5", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ydBZdxxB6K23qgw4o", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:44:26"} {"_id": "LxuGtuCZ8TZavK9v6", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n(Node -> Node - iden) in ^(adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\nadj.adj in adj\n}", "derivationOf": "CAgtRTsAqYnogEX2d", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:21:33"} {"_id": "4xhE9D6Ccnmp4AtT5", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "aBsYSu2nSoTBzHZYa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:30"} {"_id": "vxmFvR6rGwasrQHqm", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "raBirp7Tqb5BBcp5u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:55:37"} {"_id": "ydBZdxxB6K23qgw4o", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^(x.adj) + ^(adj.x) + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qhbvfzwfu2fPFvJQb", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:44:10"} {"_id": "NddK5fbwd7yzcbb2y", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\nall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Trc6AxRHMQtTtCw9D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:14:58"} {"_id": "RK9yaQbZYpG72AH8W", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SKXBoTpwPTvubgDaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 02:01:15"} {"_id": "Zc8gCRAdSjMA8S5Ph", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1, n2: Node | no n1->n2->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "7w5BWa6Guf5tgWWci", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:50:36"} {"_id": "CawnnXvb7SyY3PZJL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n, n1 : Node | n->n1 in adj => n1->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WQimqaMkMMkwN8vyy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:10:10"} {"_id": "zLJHAFysrxgGbCcqs", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WzT7soKNczJoh5mjm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:33:15"} {"_id": "yEHFemNMWzZm8NsHL", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "YJtYy7XYM4ypr2SSQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:21:38"} {"_id": "YXDCQRkTr72i4xS4k", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GbThHNvj787EPo2JT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:01:01"} {"_id": "aon4pP4mYF4x6HuaE", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in (Node.^adj & ^adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "opXv3KycneLwNSvCp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:32:29"} {"_id": "h3Zvtw27TeaCm6SoZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:10:20"} {"_id": "DXN8QKn5j6i6HTdaH", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "bHmfmhZc4SYvTyN5o", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:53:31"} {"_id": "wGqmFpvxwzFNSSzf2", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all ad : n.adj | n in ad.adj and ad.adj in n and n in and ad.adj in ad.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qzWaHYy5bokmT4TsX", "msg": "There are 23 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ disj fun iden int none pred seq sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 01:34:46"} {"_id": "mQBigoZyqFv4zg8ua", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n1, n2 : Node | n2 in (n1.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "RTZXMbuEpYjewZFzh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:55:07"} {"_id": "FM8Rwcmb2GqAWGfme", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n->n not in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "ufd7SdKBHcHPmxgPp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:54:06"} {"_id": "9DWWd3XSZjgnCdrkh", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KjuzvzgFetAznDKye", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:21:22"} {"_id": "tEA8ZZ769q2nP7NE6", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "pg83SuyYBABmYuQeo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:38"} {"_id": "Cdwnz7bTC7r2KFEYx", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n,nn,nnn : Node | nn in n.adj.adj implies nn in n.adj \n}", "derivationOf": "kDfpgKtBG4qEjhCdd", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:58:22"} {"_id": "mfta5E5GRvC5W5e3w", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tbtcKEzzux9JcZxYe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-6 20:50:28"} {"_id": "vPqWxDQFhcYrvHdwd", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj and no ^(x.adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TEH954mYEEW3oYy7r", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:25:38"} {"_id": "hHe5LaqKmtwzfBATq", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "mfJwLi2bzz75BeTcc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:46:52"} {"_id": "BxpxsFuBrjZBaR5E8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node = n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xL7ebXuSeKSenya3p", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:58:03"} {"_id": "zwpftA6GRjPqWtRb9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t^adj = (Node -> Node - iden)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zmQJaCGmHeFayAAEL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:39"} {"_id": "GHRARGQHgD55ueTCy", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "twXaXTrAfArTDLgAH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:35:01"} {"_id": "rcSKhCfXqAwtWDixQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "hsdRi7Tn5CAXX43PY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:51:21"} {"_id": "v3ywSbvwHwK27ZZ8x", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | (n2 in (n1.^adj + n1.^(~adj))) and n1!=n2\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "h6Y8bYLzcYBZrjXgX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:40:42"} {"_id": "zzu7Q2sKW3iYQKYda", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno *adj & adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aaGawNYkijcxmfqSR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:34:51"} {"_id": "3PBgMwn8X6fJKTYfZ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ybg47GHsB2iMmfrwS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 20:35:38"} {"_id": "oisjGf4FHY7ybsDNY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n adj + ~adj in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "itHwL7EyfKM27usff", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:22:02"} {"_id": "YeLDB6LTzxiu95jNh", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj in ^Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dNwMWGmgYDxL7yD5N", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:13:45"} {"_id": "h5m5ZmnToqGpWtvEZ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 | Node in (e1.*adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EqQcc6nrFgTr6foNT", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:24:03"} {"_id": "eb4HcFiqTBRi3kjPk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "ZboiRSJTpeJKtPBaf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:15:48"} {"_id": "6ig9sdDGvMtcQTyej", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.adj + adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5bKSKLQhcWJipx9qr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:26:16"} {"_id": "GF6wp6miXvF2krEbF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + n.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "udKna2mKaGqhY46yS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 11:54:39"} {"_id": "yN7FK83qxRCJTk7am", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kkbezY3YXBH6Wa8qw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-8 15:10:56"} {"_id": "SQfDMkt2AkKMq5nNm", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gZNZxog3EnERE4vF7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:35:29"} {"_id": "faYnJkMG9tX3PMyqJ", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1 : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:33:54"} {"_id": "g7fJtsdWm7FymsDmu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.^adj \n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "z7vPMf9bc2PboMXp5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:55:21"} {"_id": "bxH8etmD4mBordgn3", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1:n2:Node | n1->n2 in Node implies n2->n1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 3 possible tokens that can appear here:\n, { |", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 15:42:44"} {"_id": "xsoGD3brSP39Jk9Sz", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^ajd \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9s7r24r4MEFy82EF3", "msg": "The name \"ajd\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:35:57"} {"_id": "tECQKhXzhGNN8ToqE", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tsome adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "q2P9o3Tjjw4EnKxK9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:16:56"} {"_id": "Wg33yfez3v4pzKKZR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5wbxzjRupchJhBuJD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:11:25"} {"_id": "vzMgGsfTYnk7X4pz3", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:31:57"} {"_id": "KSuk2Lqqh5BMZtvkC", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | n.adj not adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2za94DXtwqCpwajm2", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:09:37"} {"_id": "mBDH9QRXtiEY4PjPA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \tall n:Node | Node-n in n.^(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "yNkZCf5Gu2RsYAFbh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:38:36"} {"_id": "aYnx62NPZpXKoQzF5", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rHB6gonSnQxiTyns2", "msg": "The name \"n2\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-25 16:26:04"} {"_id": "cXHk9GHmepRR5b4gP", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n adj + ^adj in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZD5RPTo6usJzwvhms", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:28:43"} {"_id": "SbQJddTM766rWkL6Z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "63p4ookYqca7E6NtC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:48:27"} {"_id": "N8ZgFyTzQJgfDni7a", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zw5t9ThfDLgKbRNeL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:47:47"} {"_id": "oQoZGLAtfNeSCFw9K", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FhW6YGCuNbtoCvYZ9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:06:26"} {"_id": "WmeCC5ZNPMP6BGFLW", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | n.adj != adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hCWfePSvhB5B7F99N", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:39:30"} {"_id": "iqshFoJ3RqsLXXjid", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some (x.^adj).y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TAtwM3FEaryJSwmJ5", "msg": "This cannot be a legal relational join where\nleft hand side is x . ^ (this/Node <: adj) (type = {this/Node})\nright hand side is y (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:53:57"} {"_id": "9MFKhcry7YKzANWJs", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node->Node in *(adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "JS6KFrbJYDYt9o3rc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:39:10"} {"_id": "RJwhaZN7h8MDREQYb", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in ~adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tiden not in ~adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "DjNcQfRksZMMfJcj4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:27:57"} {"_id": "E7gBkTkz6fLkmKHsj", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies ^(y->x) not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BQ7seeKPK5KczDvzf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:19:01"} {"_id": "o68MmhMCgwv2Rtizp", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.(^adj + iden)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ffd3Ce5PCj5wHBWXu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:18:23"} {"_id": "QJGnX3BTnZh9f6Jww", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:37:59"} {"_id": "TEH954mYEEW3oYy7r", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "r5BW8YC3n43RjLeQ6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:22:09"} {"_id": "sicFqLm5zaJqmFcWN", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n for n : Node | for a : n.adj | n in a\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:29:42"} {"_id": "hKh9tSHbyB8TQzBZZ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode . adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:26:48"} {"_id": "hiqtu7BxZsQTpyiAg", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n adj + ^adj in Node.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cXHk9GHmepRR5b4gP", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:29:03"} {"_id": "5dp4TH8nZ7YQfydAg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj) or (n2 in n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "v3ywSbvwHwK27ZZ8x", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:41:15"} {"_id": "FQzauHWBkTTkFFJXY", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj) \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fBBC4bydcgg2XEgoE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:04:05"} {"_id": "ivCGekarxS6J6aWW7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n some disj n1, n2: Node | n1 in n2.adj and n2 !in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mfta5E5GRvC5W5e3w", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-6 20:51:21"} {"_id": "JpHvjhebKNdpWMnK5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LZuQYDQ3CWhDkZmWi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:09:19"} {"_id": "FiHWy5BMXz8tfgqjE", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "gE2SthB546Q4a543H", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:46:44"} {"_id": "WRg3upuS5wqHLtPQH", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TrSqiQaeFLbD3GMGQ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:41:21"} {"_id": "R8hFugRNiLxmbgNx2", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj = ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JJDnJbq7MuNpRS8Js", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {PrimitiveBoolean}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-12 00:07:21"} {"_id": "cyTw2F9BHbyxdMiSW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + ^~adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QSuNPryP9bCEeukni", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:52:28"} {"_id": "c2XfHiHWBtSym9JG7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.(^adj + ^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RxqvcTJgxcEAxyTvi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:26:04"} {"_id": "jcBxNEotP7SqDkLem", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & graph.~graph\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "R8hFugRNiLxmbgNx2", "msg": "The name \"graph\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-12 00:15:26"} {"_id": "xZHmaw7FJpKjsFhnt", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Nod.*adj + adj.*Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "Fv2tah6dPXTTz6eL3", "msg": "The name \"Nod\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 11:26:14"} {"_id": "YvKaAnASQibQxTZy9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tundirected\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "76BEedCwKhrbv8W8D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:20:40"} {"_id": "gSkbpD2aCQXsZRG7f", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "soyJP7gSdXdnspfDu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:55:42"} {"_id": "hgT9v2rwSDbXE9DPY", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jbYNyAG3c7Pt5Etn7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 18:58:15"} {"_id": "xdkvYFGMPQf5MyfFW", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LFHegxZB5ZpkhDevB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:32:44"} {"_id": "q2X9fXbkD63y2ifHn", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fmt8C7mk3cqH8hDKZ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:39:57"} {"_id": "kkbezY3YXBH6Wa8qw", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-8 15:10:26"} {"_id": "HimAoH6MJGRi7nKmy", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "W6nno7x2gThjCKKwF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:24:09"} {"_id": "6qHwqSi3ghZ3SmLot", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "CyXGWzhdSmuNQCGuD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 11:39:19"} {"_id": "5q9xZCcQHzYs69tMz", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "ZG2wPbi8e8JEvyxRz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:52:40"} {"_id": "AtojiKGh4zNW4Pj9K", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "qfC7rEs4D4YJdKCZt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:38:44"} {"_id": "KL9k6siqQpnbFtnft", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tNode->n.adj.adj in adj\n\n}", "derivationOf": "HbEoZgnHLN4nn2WMo", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 23:04:46"} {"_id": "EqQcc6nrFgTr6foNT", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1, e2 : Node | e2 in (e1.*adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qgZXYzStzPzwqBBaY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:03"} {"_id": "cPnqreMEqv258Hqhz", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n adj = Node->Node\n}", "derivationOf": "4wZ6uc3zLpGEcZSSH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:51:40"} {"_id": "DKhZpYhshuoGSbLXA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj not in adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gqwEhcpYeJqdqCNSq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 13:22:33"} {"_id": "iYfMYurtcpo88ahhb", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "oPmkyJKEmcrWt2u9y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:36:02"} {"_id": "QSuNPryP9bCEeukni", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *^adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LHkknDMqWdbb5Pgc2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:51:54"} {"_id": "F6wdXsHtG5F27sTEg", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zfNyz3XAcJEC7sMoJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:16:14"} {"_id": "GJMNm7FBT7apbHCFh", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "76k8myGtMxZTspEd5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:02:33"} {"_id": "LGvqbFiKGiiiPnJT2", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1 in n2.^adj || n2 in n1.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n1 in n2.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "3hEKjSemQDrJSTy7u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:01:01"} {"_id": "4patEsvmc5td87kJh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ps7syFqzFjT3NpnFo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 11:08:45"} {"_id": "CwyTKz96XbKzENymC", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | Node = (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "s5tGHdW5cHHN8ft4N", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:32:58"} {"_id": "sqAycZpLvaWhuHMx5", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 | Node in (e1.*adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "h5m5ZmnToqGpWtvEZ", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:24:12"} {"_id": "DFbuDesKhoJE8Eke3", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iyK8ErnhDSZ5AsstH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:10:31"} {"_id": "CHWgPv4rJYN2L2aRk", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jw3MRXpkbdhxDRgzc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:21:11"} {"_id": "JQxRZsTfPSoCg5Ztb", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "MrLh5PEEiGwq2eCau", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:47:22"} {"_id": "pxEcbYFmRGd48SpBX", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1->n2 : adj | n1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eqzZSzBHkt5ivTpXK", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:07:58"} {"_id": "jPAoE7mhu9vy7NHet", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ut6b2YECbbZZ3uF2J", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 19:24:04"} {"_id": "W6nno7x2gThjCKKwF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KgHxmwY4LTz5TCvKZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:23:43"} {"_id": "uQNEWC3vtdLfyESsp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.(^adj+^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2zGqPrNkLq8KfmBkj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:19:49"} {"_id": "YGsTthgtDdSYTcKLQ", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ozrwf9q78A8MvfBBh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:55"} {"_id": "M7XY4kfco6JHjx5hC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n: Node | n.adj.adj in n.adj\n \t\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:45"} {"_id": "abrzRzAzyibodeq9S", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^(^adj + ^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "c2XfHiHWBtSym9JG7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:26:36"} {"_id": "2AfQpK9FuyD4wvM7v", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node - n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node - n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "PWQCB5johBc2g8TxQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:08:41"} {"_id": "wbfo9CFtoYm5BT58G", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some Node.adj + some Node.~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "xe77X59H99QcRK5Tc", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:18:04"} {"_id": "JbgscHTMywPKQvfqh", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "L8A3xJbAJ5gCG3ZLs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:20:03"} {"_id": "SZMrwJLCRnDEwQ59e", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj.adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JqR5W2rBpvTdjCEin", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:52:44"} {"_id": "KyHJiQtwSF6nTGPXE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj + ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZaKGS7EQGoHEsvaN2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:52:13"} {"_id": "8ednFzYj7MfrDppiG", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | some (n.adj + adj.n)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "seMsdesJDd8RS74N8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:20"} {"_id": "MxajR47d4JR7f9tJh", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "kgmqMnWtuc3Xc99ZB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:34"} {"_id": "tcYAiwH4vZBNqaSX9", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wHQFZoSvQHesi8XEp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:21"} {"_id": "hnmpaCmWaGmAJ3bTb", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | (Node - n) in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Q9CLnEupXy7XCC6Kk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:06:32"} {"_id": "KcHQxujFCpkJ7XPSw", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "K7kKmqBrA7kCS4EJu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:43:18"} {"_id": "kYjDqiFs3W65xPoeS", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nNode in Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:34:03"} {"_id": "jsMNuibDfZubyvNzA", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1:Node | n1 not in adj.n1 \n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Ak3pB7yEZ5SGGvMQB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:51:41"} {"_id": "P4iH3qEkPKrf24tco", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | n in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tFXCLpfpaZ3Mewwkj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:00:57"} {"_id": "sfqbaq9QbiW3zBzhz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(^adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jv64FRe8ME4P8QqSJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:33:17"} {"_id": "Xwom6c7CHuxiqYtq8", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ySfHpJqby5XLoDC6K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 18:51:16"} {"_id": "HAW3hrJZJ7jZeKgtE", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in ^(n1.adj + n1.~adj) || n1 in ^(n2.adj + n2.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n1 in n2.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "37o8miY3NLgMLmynJ", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:04:39"} {"_id": "oiGinmMY2JsWkGsaN", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bkm9Qi6wySs59LNxB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:09:29"} {"_id": "Th3Sg4ZgKyKiFby7i", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n1 != n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "k9gF87qQ8f3auxQRK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:37:45"} {"_id": "BTrgc5k5XiHFsgRYq", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a,b:Node | a.^adj + b.^adj in iden\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rpi2PDg8xa795Nywy", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:47:03"} {"_id": "wDPkE2ZEn7PkKMQEC", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x.^adj - x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3PBgMwn8X6fJKTYfZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 20:35:46"} {"_id": "q9tG7cQSPXe6K6uTt", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mvnEKm76bCQXeRWo2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:14"} {"_id": "5ECPgxkWBXYYjFNKh", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tadj = Node->Node - iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QjDhvEY2vf4SHEwi2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:46:17"} {"_id": "hhpNx2JpxveqRpcAY", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tNode in ~Node \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kGMGzxS9AGg3pwvpn", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:17:21"} {"_id": "j6ssysdvTEXpuzDuA", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "df8yD2LZGm3k684FS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:59:09"} {"_id": "Pip4TSfDsqpK4u9oS", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n \n \n Node in adj\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tsx7MPPFFK6fMGDuF", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 13:41:40"} {"_id": "xdHwrpN97tnsojeDL", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "i4bZ9QT4zNgqJy8DX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:42:15"} {"_id": "7w5BWa6Guf5tgWWci", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "vx8kyBmmMm6mHgutd", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:47:08"} {"_id": "erEqGzBXKHTYwNMZX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *adj.x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XdjxKJfTt4A27T3Q6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:29:24"} {"_id": "NYuj43BdvHtHYv4RP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \n \n \tall n:Node | some n.*adj + n.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "cFT5gsGrXhzHpRXaL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:04:50"} {"_id": "G9igdN6T3yccnfHNE", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 implies n2->n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:00:16"} {"_id": "KRcqRcgHhwGWQC995", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FBLvtAHE87pkJ4uHN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:14:11"} {"_id": "nwHa9hDtsY5ry9mog", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "QKQ3WHyYT2khuSMJt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:08:23"} {"_id": "hsdRi7Tn5CAXX43PY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "WsMkM5ZnsJzT5xYSC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:51:13"} {"_id": "cSkXjDatMtsbgnjdj", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj\n}", "derivationOf": "QpNoJewj39Qgufz4p", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:02:59"} {"_id": "powoNN5At2cNToaCr", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^adj + b.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NYuR2BGgEHCmCMyxs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:47:49"} {"_id": "YsBn949SBMjp9H67S", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tnot a.aj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XJE9LZb86oYRJTqHm", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:44:25"} {"_id": "sdoq7HzfJ26GksTRN", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj.Node in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "oNRNF2Q4eaWYG2xay", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:32:55"} {"_id": "SYPR4PutSoWm523Kw", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fPuvpXeHrR8oT2txM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:53:42"} {"_id": "guDRNzizevj6BSTgD", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | (n1.adj.n2) implies (n2.adj.n1)\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P7E6yxJmuvL8BcnoT", "msg": "This cannot be a legal relational join where\nleft hand side is n1 . (this/Node <: adj) (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:32:03"} {"_id": "ZboiRSJTpeJKtPBaf", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "r7x9mJtJCyfHBbtrF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 23:14:21"} {"_id": "mb6GodJWAHtjg3iot", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n ^adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2R2o526ZPwMMGusRW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:18:54"} {"_id": "A32phByPhWGeZKD94", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3MKXFKnNoZj6nrbDu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:45"} {"_id": "uc3kp3uJ22epn9x5B", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LKsufvh23LkXR4TX6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:12:14"} {"_id": "d6uBdw7oYLWekaPkh", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aQwx7dtLjQ8ooMMCA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:13:45"} {"_id": "628xQYZyLc5yL34ti", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node -> Node\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G3sokYvfL4JpBtXu4", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-3 09:38:12"} {"_id": "df8yD2LZGm3k684FS", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tsome iden & adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ejMnEXJL2Gs4Yd2cW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:58:49"} {"_id": "4fJnqKTsPyLTgzXz9", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all x, y : Node | x->y in adj implies y->x in adj\t\n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9cno6vejYomDELtcs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-2 23:39:16"} {"_id": "szERyomfDbJcudyf3", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n,o,p:Node | n->o in adj and o->p in adj implies n->p in adj\n}", "derivationOf": "vTeWhGrvK2odyLep2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:35:16"} {"_id": "6BKachDG2d764LHCm", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6zxhzYDm6PRMi5Azs", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:29:11"} {"_id": "2mpJRKeXJt4us4Bwt", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hi3qwPHemQy9viuvr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:26:12"} {"_id": "NqAkNF8YNjbGjEqF2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.(~adj + *adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GcZA94r9cipP6g27a", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-7 12:26:58"} {"_id": "z7vPMf9bc2PboMXp5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode in Node.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kbNxrzRWqwBdmBPyh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:53:29"} {"_id": "cnByvE2K39CmYjDu9", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vmHGZv7qbuwZdmHvi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:15:58"} {"_id": "yQticP4FgZANS5ino", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall a, b : Node | b in a.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "foCFRGZzQz7pGe3wj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:45"} {"_id": "rThNcjfwwmTrMC3ew", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "MLJDyfy83QAeqyeZn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:03"} {"_id": "R5tmP64DTv5aHmSLj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some (^adj).y & x \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ms6XHLgopSxdw956B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:11:57"} {"_id": "z66rTac8NGdTfBYjh", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:24:08"} {"_id": "quZJs39KSdL3Hm85b", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NQNv2FLszdBfecm2d", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:51"} {"_id": "g3FzjJiims86WNLLA", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BqeusERjyvWvoTH6F", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:29:41"} {"_id": "pvxBd6bgwFZ69FSwE", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "6dshFZEpbYAJhmj2j", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:09"} {"_id": "BqcDmRqNKdiD6d386", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "iAX6Hqq6GKmY24CdL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:35:20"} {"_id": "z7JvwJrzqWccwdYcm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.*adj & y.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6FdZPbFT43MeJ9qjH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:56:39"} {"_id": "cLhQw5uwk8BY8bdLv", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:16:52"} {"_id": "QrRi5Bwf7NMknbj9L", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a,b : Node | a -> b in adj implies b -> a not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tsome a : Node | a -> a in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qd3kzyBZXXRcbjgtj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:15:25"} {"_id": "y7oLkRLh7wCSCcDfP", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall s : State | some s.trans\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"State\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-30 11:47:05"} {"_id": "i4bZ9QT4zNgqJy8DX", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "sab8zkCobCi2WcCTE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:42:00"} {"_id": "qjA847HaNscTxCzDn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:27:52"} {"_id": "dFoxxa4cvsAjoq6bc", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "S8BRQxkqtg7hLNj4b", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:53:14"} {"_id": "n9Y9NtbL5xz9kihpg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x in ^adj.y & x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4P2ka4twAetKWYs77", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:18:20"} {"_id": "buk8nppcfjDWyStow", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all disj n,n1:Node | n in n1.^adj or n1 in n.^adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "56nkFLb9jb9etKncY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 12:09:38"} {"_id": "CiHuLmdaWohoFKpwp", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | (Node - n) in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nWkiWCejAYftEhFg2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:39:28"} {"_id": "Hb9KKAsHMH539yiih", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-4-16 13:53:42"} {"_id": "KDmRgxGs9Gq5uEjqr", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5wJ9iBbsBY3DqoyWH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:13:13"} {"_id": "jEiyrfthxrLJcF5Er", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:33"} {"_id": "ajL64Tr9EAPSxuCos", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n}", "derivationOf": "qgL53DYioaNMyxsYd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:58:27"} {"_id": "bn4nSyFZNpfjvxpTz", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.^adj & y^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "z7JvwJrzqWccwdYcm", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:56:52"} {"_id": "ec76DSfY3CScDBozx", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n1,n2 :Node | n2 in n1.^adj and n1 in n2.^adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8meKbJeFuZ3zM6zR7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:21"} {"_id": "tRgmp4oPbQKfzZz8z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "mvsDtLCSsxLD2xkdk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-19 10:18:08"} {"_id": "8KdT6mHXYoWCtztTN", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (^adj.n + ^~adj.n) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Q4nM45ZCH8qLFYjC6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:20:12"} {"_id": "rKT4KhpTvDAjZq5hb", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | no n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "qQBzKMLyMWJh5SXpa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:36:50"} {"_id": "KXayan5TJWWb7muid", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pkjkudK7MdQN3pXRD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:14:40"} {"_id": "QNyLcridNnahyXvC5", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ogTBbTtwsGyheeaRz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 08:59:19"} {"_id": "yrBXRRCHD2qJAiPv8", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tNode.adj != adj.Node \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qbQBAMqapbS7XCQer", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:51:07"} {"_id": "XxddJhGvr9AEDfZoc", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "A8SpRBG7ZHvqjNyHb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:32:32"} {"_id": "zczBFKsj9QFvS58SA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "j8dXSKufYdNSSFNy8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:54:46"} {"_id": "mfJwLi2bzz75BeTcc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "ARDzqpQB2HfvrCaKs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:44:21"} {"_id": "N8XbuXoXqHRc5XPSC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node - n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n}", "derivationOf": "2AfQpK9FuyD4wvM7v", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 18:09:02"} {"_id": "oNRNF2Q4eaWYG2xay", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\tadj.^adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "ANBRQkMJBH2DYTaRG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:32:29"} {"_id": "KR2tH4oMaeBKhmRdE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "KWdFpLWWGqZZys3uL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 11:07:24"} {"_id": "NMRESLs78RoQBXhNk", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj + n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n1, n2 : Node | n2 in ((n1.^adj)-n1)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "mBu2oZwk4g98oTSi8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:43:12"} {"_id": "PtZt9567diAzXrCMK", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:25:08"} {"_id": "tdz9n8y2AubWDxsho", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\tall e1 : Node | Node in e1.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\tall e1 : Node | Node in e1.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1 : Node | e1.adj.adj in e1.adj\n}", "derivationOf": "AeiaTwwXMoYFEpFzT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:07"} {"_id": "DZDsf5tcKiuaw9PQi", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj no iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TMC96HEiCuLsztpy9", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:47:42"} {"_id": "2ivMGKDFS8P4iXz9W", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.^adj = (Node - n)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Z6b9MoyiYgJoBBbuQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:11:44"} {"_id": "529uzPgL5PJpaa356", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a not in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:14:50"} {"_id": "zsieAehvd5z7ctvxs", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + e1.~*adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6ssqBggKApWe67Lsy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:20"} {"_id": "uRERRoinNqPhyMqRo", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "69FSJ3oP6zJgxBExW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:13:27"} {"_id": "7LAkLrzAxuxqJsNHQ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj <=> n1 != n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Th3Sg4ZgKyKiFby7i", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:41:10"} {"_id": "KmqEzr3xiBCS5n9o7", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no ^a.adj & ~(^a.adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "itgmEii7jRfo8DW2Y", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:24:09"} {"_id": "kWqt4eDoPN9rZXkcK", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "qBMqD2h3rhvu2j6ki", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 11:17:18"} {"_id": "EdNY8xKH5XtkfS8sw", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall n:Node |Node in n.(adj.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "2PCmX2bfo7Ac8CJXx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:37:09"} {"_id": "EykLzWSJguJMiwJkA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iNHvH4LjfaM24QEWT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:17:06"} {"_id": "rXcbNYbwm7qtmiNyY", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n,x:Node | n->x in adj implies x->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n,x:Node | n->x in adj implies x->n not in adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QbEDEPZnrKrzAY7ks", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 18:16:25"} {"_id": "WTZSNskZBgpb4Pzqp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "G4Y8Yv8dPphdBCBPa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:25:39"} {"_id": "gzvWRdMjenGgzmTDs", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "GB87Bxscg7DENFuYT", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:04:18"} {"_id": "CN2Z4RDRi5yWR9QwN", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | n.adj in adj or n.~adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "eCGqgNzfHdzkYDMjE", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:12:49"} {"_id": "vaD3kGM6DeHKDyuy9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | ^adj.x in ^adj.y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "N5Qy6qw7RnB3HdNnx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:17:15"} {"_id": "p8s2Ndwdi2HQK2Yez", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "K3n3TNMHdYmLMJYDe", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:21:03"} {"_id": "ETn3sydhWzAEkXo3a", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tNode.adj in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CmHToyKbPuXZSn9hD", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:02:02"} {"_id": "wHQFZoSvQHesi8XEp", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall e1 : Node | no e1.adj & adj.e1 \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dXyMHkamAPhfWtgXh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:09"} {"_id": "Kov8hD65s7dsuLm8i", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "iYfMYurtcpo88ahhb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:36:06"} {"_id": "MM5KnTqBWE87ALdR7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Yb7i5wbLrzLrmgGrZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-4 16:30:50"} {"_id": "pkjkudK7MdQN3pXRD", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t~adj.adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fS3oRuNafFfKtm2EL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:14:17"} {"_id": "uzkJJdBg7rqESLcRS", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n all a,b : Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dEmjXuubqBFpDrtCc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:20:17"} {"_id": "Eo8BbHC5eLLsqz8BY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + (~adj).x + x \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A4siLicMRu7wLjFSD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:54:02"} {"_id": "6JSoppwmCeNt95Fmn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | n->a in adj implies a->n in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.adj in adj\n}", "derivationOf": "3tv3aioKHxLBTpCtE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 11:14:48"} {"_id": "Sbf5KkhBTYwKKCk8k", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^adj + n^~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dgxaYiZb4bwJpgxqb", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:22:58"} {"_id": "gyBaFJbzhzfanQpjn", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.^adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "RtxzR35rF6eCztgRP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:32:59"} {"_id": "LdSo3tCNb8geo6mwu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wSYT7CJ9tau9bWGii", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:38:45"} {"_id": "PCHukSp2SBqHQJNgw", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node| b in a.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Z2d6odytdWiSHNDjf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 15:31:29"} {"_id": "KNMD3RSXrkEopafo6", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YZt46FwWbQY9EkbSa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:25"} {"_id": "JytpjETstMNBorg8j", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n \tno adj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RNWm9rLAbNdf7HxBC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:14:24"} {"_id": "bQ4ywFrDe7e5EzRWC", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MeFa8bC4mgjDXQQBu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:57"} {"_id": "tPMTAatjEyadf8Z72", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HpyMJenJeoyZPikb6", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:43:15"} {"_id": "98nWXmKKmoouseMnx", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a->b in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fJYwKe2yYsXius76A", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:48:18"} {"_id": "HFg6m88fvcQ3jES68", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ziKMkjXhMeQa5QDqd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:23:10"} {"_id": "LxpDp5QjAo3kWMaEj", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "WFMWrqSsukK44MdzD", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 546.2500305175781, "y": 199.1666717529297}, "Node1": {"x": 182.08334350585938, "y": 199.1666717529297}, "Node2": {"x": 364.16668701171875, "y": 199.1666717529297}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:56:28"} {"_id": "A6JPPEMcwhQyPSrvC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | some ad : n.adj | n in ad.adj and ad.adj in n \n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 01:33:50"} {"_id": "vDA5CYeJXSJdGMqMD", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (some adj) and (Node = (n.^adj + n.^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (some n.adj) and (Node = (n.^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "h8pZa5Ap56t4HkDax", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:50:33"} {"_id": "4pjygyxeg4SWyTEcD", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n : Node | (one n.adj )&(one n.(~adj))\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LyDCCt7m9T8jtJFWq", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:28:19"} {"_id": "r9d7wkqGkds9Wwtje", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | (n.adj) in Node \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DZkrgwsAsipzuQMWj", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:28:32"} {"_id": "3FYq4zrapSmAAezxs", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | adj in (^adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nGqZNwzeAa4CXCfx7", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:46"} {"_id": "JAKjA8EQMhziAtCCz", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "mQBigoZyqFv4zg8ua", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:55:23"} {"_id": "CmHToyKbPuXZSn9hD", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tNode.^adj in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nRYTqBShetajwFeH6", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:01:30"} {"_id": "EmreY8shF7ficgSKi", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | (n2 in n1.Node.Node) implies (n2 in n1.Node)\n}", "derivationOf": "FiHWy5BMXz8tfgqjE", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:48:05"} {"_id": "fkJ3kLAo8aEFnRPiE", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.*adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YbbjjZFEnQKtHXxta", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:53:09"} {"_id": "y6akAbhdT4qQLAepF", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node - n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kET9ASnj8AYadE8nx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:59"} {"_id": "JgRNLghuAA6s5M8hk", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t(Node -> Node - iden) in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tno (adj . adj)\n}", "derivationOf": "hAqqKfjL8vgrjEwGq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:29:11"} {"_id": "ZdJY8aB2xYbgMotfa", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "Yd6D5Csz5Y23A66Ck", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:09"} {"_id": "C4oN8bmpNmpXX6tBv", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj & Node\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JcJEiJ67rPLSht6oM", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:32:51"} {"_id": "TntB5AyBZejbTQHW7", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n, n1 : Node | n->n1 in adj => n1->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mpxTjaQCfRaygXK4w", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:12:28"} {"_id": "jZcmQSgtQ5BPorc9n", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "R9L9HBJC33gHNpy6C", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:05:35"} {"_id": "Wa7EfaF2zg2A3xDQD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Mz88Q8cctjN3mGk8q", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:27:50"} {"_id": "SRvs9ZbKw6uFSNzrQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "8mmx2eukmRRyi6jTt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:40:38"} {"_id": "rSFtHpie6fzAoewfc", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^b in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "qDD7bcrKHMLZ26L8T", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:00:44"} {"_id": "wbBxQts99bmgNYuzE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\tNode in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "iwzaD4guRZNCYqrsN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:07:58"} {"_id": "iWYN82N5ApWtWQtxB", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in (Node.adj & adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "9K4LjKYqWKzKp2diW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:29:28"} {"_id": "NjtJSPfExGCP4JCad", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & (~adj).n)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FoJ4YhexBuNKErmgR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:07:08"} {"_id": "HQexxqSoXqFQyiPrJ", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oQoZGLAtfNeSCFw9K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:12:41"} {"_id": "Jf6ZR7Ebjmgae6LFm", "cmd_c": true, "cmd_i": 2, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}\n\nrun {oriented} for 3 Node", "derivationOf": "aPqh9NetcAZ6WQu7E", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:52:49"} {"_id": "s7kikQSzfN6vAQyRf", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.*adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wQx8hFpRqbc3HJent", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:18:40"} {"_id": "MbZKoYdNoXbXow28i", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.*adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T8WeWwoJGoaciyHWi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:50:33"} {"_id": "8cm9R8hFwrbsXKpMB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "cb9QyomhJhKNxGCg8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:54:26"} {"_id": "cb2nuCshcwujf7WwS", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MNwyNtTMJ3XnjnGLH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:20:29"} {"_id": "nsNzFJ8KCF8KBHoYT", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n in n.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xvmti93o94B2nsGYS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:57:19"} {"_id": "h8pZa5Ap56t4HkDax", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (some adj) and (Node = (n.^adj + n.^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (some adj) and (Node = (n.^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "8zwjq3wXE6dMKJ6p2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:50:12"} {"_id": "rfXa7BruPqMqgiTHy", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n != n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:13:13"} {"_id": "HirsiNK86tfHpqgDg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x & (^adj).y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AQ5rKKddAQSJ7SXYm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:12:20"} {"_id": "fmt8C7mk3cqH8hDKZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "p2oqHdqZkbam9J5mv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:33:39"} {"_id": "7bqE3SuH9a4bJPqAC", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uc3kp3uJ22epn9x5B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:12:20"} {"_id": "WWGPCCWdjCrCouico", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in (*adj - adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Cx49Qtkwk5DqojG7D", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:54:10"} {"_id": "PHW54hN4cq6Se8HbP", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n all n : Node | n.adj.adj in n.adj\n}", "derivationOf": "gShgsFcyQZFcgPxJK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:51:05"} {"_id": "cSxKJwM8d8kweoYac", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj in Node.(^adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2ik4jWhnqBYAia4AJ", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:16"} {"_id": "sg4wa6ELs5vwDR3dp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZF5qBnHmB3gbokaZi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 21:57:36"} {"_id": "oH6DvoxZYyEDznAH8", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno Node.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "heqaNBmBoyrHGCsRb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:56:25"} {"_id": "eb9wnsJHEk2ytDkFN", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8KdT6mHXYoWCtztTN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:20:23"} {"_id": "4pDiLoTkBxGXFep8M", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^(adj + ~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "kLKgqynmf2D5Yt3md", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-19 10:21:13"} {"_id": "FRQzokAiAztnzi79q", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | Node in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Aq8MxyYK4XNwcd6Hf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:32:53"} {"_id": "cbNa2jzLbS8NmqqZZ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "96ob6vuBp8LLYns42", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:47:26"} {"_id": "GxaZaANgaJy7sAdgr", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some ((n1.^adj)->n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "CFEXupWgghvfe29j4", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:52:26"} {"_id": "gqwEhcpYeJqdqCNSq", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 13:22:09"} {"_id": "qwXXZXrCCqRSWByud", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall e1, e3 : Node | some e2 : Node | (e1 -> e2 in adj and e2 -> e3 in adj) implies e1 -> e2 in adj\n}", "derivationOf": "ZEksX3b8edBWimwBn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:33:20"} {"_id": "baH3uFCgeqYhh8mE4", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "eyAfGvKE32ps5kyov", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 444, "y": 265.3333333333333}, "Node1": {"x": 296, "y": 132.66666666666666}, "Node2": {"x": 592, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-11-11 12:02:19"} {"_id": "bWexm3do9Facvimi4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "s7kikQSzfN6vAQyRf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:18:55"} {"_id": "S7DsEc6RFAv8icrdh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.adj + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AAJmbvnQcpffYmiJW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:55:32"} {"_id": "5T6nZXZHuEDzrPzfA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NjtJSPfExGCP4JCad", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:08:40"} {"_id": "A2n2LKQ6Jg7qy34AX", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WgW3kqbYypLS8DeZq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:00:13"} {"_id": "G9iHtZCTosD5nNZTp", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eKcGuNeCfpzitPXai", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-9 22:23:27"} {"_id": "hYchoC72To49nLZyr", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nNode.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6x3oLrYxk63X6pZ5f", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:26:47"} {"_id": "LboWQx9RPw9C3TrRi", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n, n1 : Node | n->n1 in adj <=> n1->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TntB5AyBZejbTQHW7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 01:12:59"} {"_id": "J9YLX4ooC69fp4xuL", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n:Node | n !in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n !in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ivCGekarxS6J6aWW7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:52:10"} {"_id": "uN2ZqJwQTKh3Nw6Ez", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zBNM5gXPyXJRc2DHr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:08:11"} {"_id": "7692guzvutgRFyvme", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GkK4Nao4vXH862xJj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:30:23"} {"_id": "bB7B4PegHxwWbwP7G", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5gHXhaTQxtWN6wd6d", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:48"} {"_id": "XJE9LZb86oYRJTqHm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "k9W74KTfPeCkNm3gf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:45"} {"_id": "DgqzqwLH7wXBDFBA4", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Gfe7t4qqsT9ptRDTk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:29:52"} {"_id": "h5P9JRaEGCAqMcuBG", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n adj # adj + ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P8L8MqW8TY2ynj99F", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:48:15"} {"_id": "FEoZyzPCeeWTxvTS9", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tone Node or all n : Node | Node in n.^adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "YvKaAnASQibQxTZy9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 23:40:30"} {"_id": "WsMkM5ZnsJzT5xYSC", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "yPoqq6ErZvhi2GRB2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:51:02"} {"_id": "LRTrH65DyKuDLw59g", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | Node in (x<:^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yZSyz9jZaE22KZR2x", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:54:33"} {"_id": "FoqDPtf6bv8tQJ5rw", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n,x:Node | n.x in adj implies x.n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This cannot be a legal relational join where\nleft hand side is n (type = {this/Node})\nright hand side is x (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:15:18"} {"_id": "b4kcDwN5FMNxsZhtu", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "LxpDp5QjAo3kWMaEj", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 546.2500305175781, "y": 199.1666717529297}, "Node1": {"x": 182.08334350585938, "y": 199.1666717529297}, "Node2": {"x": 364.16668701171875, "y": 199.1666717529297}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-1-8 21:54:40"} {"_id": "cYRCGLf9MYDjbrp7z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in n.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "55QmwvEATxm3MFHxe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:29:14"} {"_id": "kgWxHQafMoshdhwcp", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | all a : n.adj | n in a.adj\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ithXeBTGPiCrMzqhX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:35:24"} {"_id": "XQHyQnFr9mTMccT59", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "TJmP4Q4Ri5oAvekzK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:52"} {"_id": "ZpatMPg7MrCezdAEz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "AtojiKGh4zNW4Pj9K", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:41:17"} {"_id": "gf9T5hDj9WKjCxfAf", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n adj != adj + ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "h5P9JRaEGCAqMcuBG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:48:32"} {"_id": "76Me9R6wKKkBzJ8RK", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | (x<:^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LRTrH65DyKuDLw59g", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 07:54:41"} {"_id": "JPWgRMRsKjArpYmQ8", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n,nn : Node | nn in n.adj.adj implies nn in n.adj \n}", "derivationOf": "Cdwnz7bTC7r2KFEYx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:58:28"} {"_id": "GqjAs5f6KYvitMn7T", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "y6akAbhdT4qQLAepF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:27:20"} {"_id": "rcgyosQTwm55Ezaor", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node = n.^adj + n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "cjgB5DJEJhGuGc4cs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:43:04"} {"_id": "Xs6PXK5B7gm5EbWkj", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HKqBeGTGiftBKXtSS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:32:40"} {"_id": "BAdEsqgpkhPEAvYwZ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n all n : Node | Node-n in n.^adj\n\n\n\n\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dsPdjsmgwYTZy3dDe", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-2-3 07:35:11"} {"_id": "8QKgPrG4fpDCvRXcA", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node | b in a.next*adj\n}", "derivationOf": "cxXfBqPuxiEFCJ65x", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:35:13"} {"_id": "y8MeLPSDgxYnydeLJ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n no ^adj &iden\n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zGakZwnPfMSoyxvgv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:41:47"} {"_id": "gEzB5ZAjTNBx3zW24", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n.adj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uk2RtKSThbHftbZrp", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-12 11:08:27"} {"_id": "hZwMRge4byE79Bx9F", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:42:43"} {"_id": "Hamfo3gTXyB3sQykc", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n Node in Node.^adj\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rpDG3d3Q6nuNzARF9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:52:35"} {"_id": "hiBAdB6dKFFxwrP2R", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y : Node | x->y in adj implies not (y->x in adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2FWzBhMA9XJFAaK3r", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:40:15"} {"_id": "dTatQNDGS2tba2WGA", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t^adj\n}", "derivationOf": "f8TzvFQMvFtWau69Y", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:57:27"} {"_id": "ZHgRB7HdX29c4Xicp", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no ^(a.adj) & ~(^a.adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KmqEzr3xiBCS5n9o7", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:25:30"} {"_id": "LqSREJN33XvHQkGwd", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n2->n3 implies n1.*n3 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "kGTGD6TZmrHsAGZd6", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:00:20"} {"_id": "wCQGFjppqsFuq7hwv", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bADKLYN3axm6K7S9D", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:58:44"} {"_id": "p5yYeKoaEqt6usG8i", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^adj + ^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "DNbRpL526sZr6joBf", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:04:06"} {"_id": "yR9qScjw4yEABE9Z9", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in *adj.Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HaJyneC6dW2N23coS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:35:29"} {"_id": "oXGjQ4YXhus8w5hLK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.^adj + ^adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eYNSESfAcZzKkiyq6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:25:07"} {"_id": "QRzXFMb8iYQRGCJ93", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qEjpYo4nagjLuJNXZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:26:49"} {"_id": "tRHcTP2tSt48J4PAF", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "SRvs9ZbKw6uFSNzrQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:40:52"} {"_id": "FmPdNNChMgN5NxHgg", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n: Node | (n.adj->adj.n) in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZD8HSoi93mN7rzaSR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 08:58:00"} {"_id": "4D6f5mM2m82EDBHw7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.^adj || b in a.~^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NkzAZAqjqQ4zH5677", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:00:48"} {"_id": "KxWiDfjkjBFSN9nsD", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n2 in n1.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "uv58BmvqFQyHuRhx3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:41:39"} {"_id": "K3TtfSyupA3XH672Z", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x<:^adj & y<:^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bn4nSyFZNpfjvxpTz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:57:04"} {"_id": "KtMRpXiKqME5J5Ke5", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode->Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pXnkSAXEqMELBAgNJ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:36:13"} {"_id": "jxETmstg586Ez7fZw", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "oF7nFAgMDeTK8dCJ6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 11:17:13"} {"_id": "tsx7MPPFFK6fMGDuF", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AB6Mm9aS9gvFGs4Q9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 13:41:19"} {"_id": "MMpgCXocthGHk2e6Y", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*(~adj)).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "S7HEvj6bXEYMkbZMd", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:48:50"} {"_id": "6fcusjn5E8xXG5WBD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj or Node in n.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vQhvMRD9uhZyx5xPK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:46:22"} {"_id": "hnKJvuirvyZHeZeLs", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in (*adj) - adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WWGPCCWdjCrCouico", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:54:23"} {"_id": "dgxaYiZb4bwJpgxqb", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "D4vLGsHBCMLAfuDqH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:22:17"} {"_id": "s3x9FFkXFFxP3GvNX", "cmd_c": true, "cmd_i": 1, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node - iden \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "nhpXLgrvi7XnpPuSN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:03"} {"_id": "oKR5MqctGpZXZwy76", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "pxu2xa7XFGKmRvDHF", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-8 19:52:19"} {"_id": "QbEDEPZnrKrzAY7ks", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n,x:Node | n->x in adj implies x->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FoqDPtf6bv8tQJ5rw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 18:15:42"} {"_id": "Tr6P6habsLAuqWEv6", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj && Node in ^adj.n || one Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "eb4HcFiqTBRi3kjPk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:17:24"} {"_id": "boZYAe2EKhP5FuwS7", "cmd_c": false, "cmd_i": 0, "cmd_n": "run$1", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all a : n.adj | n in a.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\nall n : Node | n not in n.^adj\n\n \n\n\n}\n\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n\n\tall n1,n2 : Node| n1 -> n2 in adj\n}\n\n\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj \n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\nrun {}", "derivationOf": "f8qntQBEwRD4k7aeb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:17"} {"_id": "froNtQRxCWe3JvMPq", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "icTvGFwW9Jn5Caogb", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:08:59"} {"_id": "4qSTjaM5EBBbWdKQS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n one Node or all n : Node | Node in n.^(adj + ~adj)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zKJB9aKBvBqKzGafy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:25:12"} {"_id": "43MbLspQCmiEdhyhF", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nall n : Node | n in n.adj.~adj\n }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ndTXiSNNL5aDcbsr6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:14:23"} {"_id": "tY6vWuTtCTYKMHvrR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | Node in x.*adj & y.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dY8W9hca4YsLPEmoQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:56:12"} {"_id": "3vFojw3DS3hpKTGh7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SwK2To457So9W495A", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:22:39"} {"_id": "R7BcRop7gzPrjuReG", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a1,a2,a3:adj | some a1.a2\n}", "derivationOf": "YtLLCLkjwTQePSywp", "msg": "Analysis cannot be performed since it requires higher-order quantification that could not be skolemized.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 15:21:13"} {"_id": "SXCFi6jE8fccmpKzQ", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XdXPGH3QQTBTyeaat", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:21:03"} {"_id": "kszYZvCNBHmZNwECP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tsome adj\n\tall n : Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hnmpaCmWaGmAJ3bTb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:06:48"} {"_id": "N3kSKDQyeJrtoktMx", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oFxkzRSAmEueSvyaz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:31"} {"_id": "3N4tWg44drai5ZCLt", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | b in a.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "biNBpSd9d9omDN27p", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:02:11"} {"_id": "L6ms2nzPhmPsb4xsg", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bkFZjQfLFwd2WhoG5", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:30:03"} {"_id": "3hxeenrzJLz43DWow", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\tsome adj implies Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "wbBxQts99bmgNYuzE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:11:07"} {"_id": "iwspqeJdQb4aHuhbZ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "Eq8XhpBARoF8gQmfL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:17:59"} {"_id": "tZyz73y3ALaLEtD7H", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj^\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AjviLmGTS2GDdAZXX", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 22:51:14"} {"_id": "Jxo79wmTzrwGXxcwK", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:13:00"} {"_id": "BgDPuEvqqTLgbpDQj", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | some Node.adj or some Node.~adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "yK7acPp9AMgiY2t8e", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:17:46"} {"_id": "2kQE5trafm6kMmf2h", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 10:54:01"} {"_id": "eAjRQJbeBLESGydth", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode.adj.~adj.Node = id\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tnot (Node.adj = )\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hTLNqwnhyodDB9Pvh", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:11:21"} {"_id": "5gB4acASY5jnRvzat", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uJ8HLkcTPniJjSHWE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:35:28"} {"_id": "soyJP7gSdXdnspfDu", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pfC4igj9xwMN7DmfC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:55:31"} {"_id": "YkPyGD29f4sHMaueX", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KsCsTSheNYehn5ose", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 16:48:37"} {"_id": "xbZ9ZDX7iB7s7d3aY", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Z4yvcviJQZGr6R4uQ", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:24:12"} {"_id": "xR9sgNgL6Rk7cSAGR", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xsoGD3brSP39Jk9Sz", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:36:04"} {"_id": "QJhGYQgFoTbSAd7vt", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T3bn3xPeDbXAxpFop", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:52:23"} {"_id": "5CZ9KWBaHPeXBdntD", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in adj.Node & b in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qS42e7GvgKMH6NpjB", "msg": "The name \"b\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:38:09"} {"_id": "y3QZXsq6g9FzmSDM4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n \n no (^adj & iden)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj \n}", "derivationOf": "e5PiXNEdeSWdTh5Cp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:29:53"} {"_id": "sa32uQE8AfCJDBX7W", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node = (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node = Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "3ySsvPh3fXLL38YXY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:42:49"} {"_id": "TXo8dfXweDvXQQfPd", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9wPELfwsqAgLqTE7Y", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 18:59:53"} {"_id": "m9rQzonu2a2EYCCWa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a not in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NTKcueytcQtwhNjJt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:15:45"} {"_id": "pEi8hiTALqGtCfi7D", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(~adj +adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NqAkNF8YNjbGjEqF2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:28:10"} {"_id": "24kzkZoATsJK2Jkbj", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n all Node.^adj\n}", "derivationOf": "uxMhnWmzsfL5RRxwc", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:56:49"} {"_id": "csN57YKYRKy9kfs7o", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Nodes | n in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KTNCkrS8LSbuzPwbf", "msg": "The name \"Nodes\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-9 22:47:37"} {"_id": "5KYTD6LvDL8HBqFnL", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | not n.adj in adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tsiY9ihcWckyThBgT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:12:53"} {"_id": "CAgtRTsAqYnogEX2d", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n(Node -> Node - iden) in ^(adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZvhsnrRLmGNqRo98c", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:20:46"} {"_id": "xL7ebXuSeKSenya3p", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n = n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oGSQFYZaYwmeWBWhe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:57:56"} {"_id": "ComPvPPfGGhWHiw2d", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dnAw8iqyumxv6i7tH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:23"} {"_id": "9s7r24r4MEFy82EF3", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^ajd \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2jtgE9EzygZHm8CxN", "msg": "The name \"ajd\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:41"} {"_id": "qPs9qFpJpQnoy2eYG", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | Node in n.(n->n.*adj)\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "yQstKD8HPgH5jYtrS", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 444, "y": 265.3333333333333}, "Node1": {"x": 444, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-11-10 16:51:37"} {"_id": "qDD7bcrKHMLZ26L8T", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a->b in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall a,b:Node | a->b in adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "xxnXKcK4LbEAiG3Xk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:00:29"} {"_id": "aaGawNYkijcxmfqSR", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno ^adj & adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "74DtpnptG6TCyBeZ4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:34:18"} {"_id": "zrzTjq5pjHvfTt5gW", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "irRXcj4mXFhmubfG5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 16:57:38"} {"_id": "iGu2TdxwKsCwEWaPC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-8 22:15:45"} {"_id": "8wnpiTcHwwodnGuz4", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "JLgRTX48eEJBY2xsk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:31:01"} {"_id": "aEo7rjgkWGZ8qRrJ7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n: Node | Node = (n.^adj + ^~adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CwyTKz96XbKzENymC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:18"} {"_id": "8xcnh4pJbv3ySLbjq", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n no ~adj.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P8kjmvS5xcP2jFgv5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:46:36"} {"_id": "jEBo9TcxYCkKDT8B8", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~Node.Node in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:46:53"} {"_id": "RvtcEFRENBnkpDdMc", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "N6RTGkTTDZGAPSRo2", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:07:45"} {"_id": "ZQfnABEnqL5BjocFS", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.*adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wTnEQZpHwDtqXg9KJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:45:07"} {"_id": "raBirp7Tqb5BBcp5u", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tsome iden & adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7QFjPrgig4PuFouAA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 10:54:27"} {"_id": "JSrKFvgKSAn2x6ZCT", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "3ZmTCB9kLgqJQc7FA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:01:27"} {"_id": "HyZzkJAMZspCMchfc", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in adj.Node & n in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5CZ9KWBaHPeXBdntD", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:38:14"} {"_id": "hmNsbrM6fGvwBTqyi", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n : Node | n in n.adj.~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in Node.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DMkFA5zkzKsfQZGnH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:53:54"} {"_id": "bxkabv6z2qiJCZpyz", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n adj = Node -> Node\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | all a : n.adj | n in a.adj\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kgWxHQafMoshdhwcp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 13:13:04"} {"_id": "3hEKjSemQDrJSTy7u", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | (n2+n1) in n1.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "KxWiDfjkjBFSN9nsD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:06"} {"_id": "xpf4gzd4yCSTGhWeo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "eHSj4hDRMwnQWs3mh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:45:24"} {"_id": "8hY9ca88DXqdfkoQo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2khwuKcYMQkmn34bH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:30:20"} {"_id": "7yLuH8kpFZN47uDqz", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj implies a in ~a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "y5m97H8jwTMrQ5ACu", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:37:30"} {"_id": "NytGbdE3bu2EzeL9r", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n = n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BxpxsFuBrjZBaR5E8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:58:14"} {"_id": "tvNTxceFyDFgcxypY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n *(adj + ~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "TFH2x8oSYsWnhwFG3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:22:43"} {"_id": "Xwe97qC6hgX9vtfNK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.^adj\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zqw65Qhn7e7D4kbgP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 17:52:51"} {"_id": "PpP3foJbmGZTNGAzD", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "FxdGN6eMz4xrKwptu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 19:02:38"} {"_id": "8X4nPngt82SahYyTF", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pXWWtLsQfRNe75evo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-18 22:01:05"} {"_id": "D8qpy8dgeeXrXQtNX", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TBdaJZsFWnJKy6awm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:43:02"} {"_id": "wgmJKxFqHxRNN2bpC", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(^adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qQubEMmJyjqNMCSqW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:02:20"} {"_id": "HZbAh7ykzzne6qkNR", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tno ~adj & adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zzu7Q2sKW3iYQKYda", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:34:58"} {"_id": "qaGr6xZPwyGZkumjF", "cmd_c": false, "cmd_i": 0, "cmd_n": "run$1", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}\n\nrun {oriented} for 3 Node", "derivationOf": "cwBoxF3c3cJs8Z8xu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 18:53:14"} {"_id": "D4vLGsHBCMLAfuDqH", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eb9wnsJHEk2ytDkFN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:20:38"} {"_id": "QFsobGWiAxKdapatQ", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t^adj\n}", "derivationOf": "AZMFvgikYEPPNmrxQ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 09:34:53"} {"_id": "QmtwQAx2LSKPzjpeB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hiBAdB6dKFFxwrP2R", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:40:59"} {"_id": "9PJWKbiDGtS9faxXi", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "i6Me2AgW2sM2zBrzR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:34:44"} {"_id": "2LyPcqmJ5QyzpJaTm", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tiden not in ^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DKhZpYhshuoGSbLXA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 13:23:28"} {"_id": "RTAobn7tMhyajmWoW", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "umLP8soNCKRirggdX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:12:19"} {"_id": "GwGTvsFJAGesBwTbG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in n.(*adj + *~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "RAck4rpyTeCvC6RC2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:44:11"} {"_id": "Fc9C4ZH9ByJjfgaHQ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "h3Zvtw27TeaCm6SoZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:10:32"} {"_id": "kET9ASnj8AYadE8nx", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nNode.^adj = Node - node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hYchoC72To49nLZyr", "msg": "The name \"node\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:26:52"} {"_id": "fRG2qTaKQMQwmWxB9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "z66rTac8NGdTfBYjh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:24:36"} {"_id": "FPWivqvB62cmvb77q", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:54:49"} {"_id": "jdA5L2cMb89HceY2J", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zrzTjq5pjHvfTt5gW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 16:58:45"} {"_id": "Qhbvfzwfu2fPFvJQb", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^x.adj + ^adj.x + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9x7K3rrq9QApat6GW", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:43:57"} {"_id": "2HvLiy4Y5mk8vrTRA", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4NEcnKQaMqpQs6bnA", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:40:38"} {"_id": "eNtX4q7f7vuxzdtXQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | (some adj) && Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "Sg5KfhFHHuzmfecxd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:34:38"} {"_id": "JLgRTX48eEJBY2xsk", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj and iden in adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "uwqwR6EXx7s3jWZzS", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:30:52"} {"_id": "jpPcbP7Fdep4SRLQQ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x & (^adj).y \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HirsiNK86tfHpqgDg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:12:33"} {"_id": "E2hDiGQjvMhX8Xxba", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SJ3WGF6MLtaBNfifk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:10"} {"_id": "uGG2YYaL2QWNCw4fz", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pkfBoSwS8S6ZqwvEd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:14:35"} {"_id": "hvBGucb8ERYXibtBL", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node) + (n1.^adk:>n1)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "jZAEzzYqYB4Q3DBxf", "msg": "The name \"adk\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:29:27"} {"_id": "WsNeBoevgMHXyqP4v", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a:Node | a.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "WFMWrqSsukK44MdzD", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:59:48"} {"_id": "98A8tocBXmbKmtDjY", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in trans and n2 -> n3 in trans implies n1->n3 in trans\n}", "derivationOf": "R7BcRop7gzPrjuReG", "msg": "The name \"trans\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 15:22:00"} {"_id": "vmHGZv7qbuwZdmHvi", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BhgAvdrLQuK46tzK8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:15:36"} {"_id": "cfsvMBreuoRMZSZZy", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JsaW5q5Bmdmsqy9k3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:48:27"} {"_id": "t8nGNEt5rnKCfqQP2", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in adj.n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zBqPXRijRo2my3viA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 03:44:15"} {"_id": "gGFPZu3t7P3vEALnN", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall n:Node |Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "feaFCRx4FFbhXXB5x", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:40:19"} {"_id": "hNkjHgkLZmH29eio8", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^adj + b.^adj in iden\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BTrgc5k5XiHFsgRYq", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:47:11"} {"_id": "P8L8MqW8TY2ynj99F", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 16:47:01"} {"_id": "hRZLCLxa8SDNNAcyj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "6QamdBATgY2rmSHi6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:48"} {"_id": "9thruSvCn5kvpjHei", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "PWBHYLFaMRmcdNFu5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-21 10:32:58"} {"_id": "D7MdtgTBnwhnGFMJA", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "J6gp5Km8wrZo7MdMu", "msg": "== is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:07:39"} {"_id": "Ljz9qidxHYfgrr5mX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all x : Node | Node in x.^adj + x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "zPqFCqDqN8amgcZgo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:08:37"} {"_id": "MxP2mXbkGLRJswuJQ", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not int a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Eft3Q6BZ6aEjQ3tPJ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:35"} {"_id": "wt5pKWW4XjEMxa3XR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj != ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9DWWd3XSZjgnCdrkh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:24:05"} {"_id": "aDD8qcJj9jbQZe2o5", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vHnTj3G4Jp8sGSNWY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:15:52"} {"_id": "xWY2rGRM2euSXPSpr", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:02:17"} {"_id": "pXnkSAXEqMELBAgNJ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RGk73q2rQQNKsZ6hB", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:36:04"} {"_id": "c5evJBaFvMh5eki2W", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \nall n : Node | Node - n in n.^adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dcpYyj92Xk2xwuAfD", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:56:49"} {"_id": "hPNSddghsyMp5kYh7", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n->(adj.n)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FzGfXJ3h3CXyoNRCh", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:36:20"} {"_id": "xmRwm8RC7r2DENJtg", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "pvxBd6bgwFZ69FSwE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:25:27"} {"_id": "udKjyhy9orThvhsR3", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = no Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xXvE5C4hw2rmxpJiM", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:46:12"} {"_id": "iH2Tn53saZrzn5QGa", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cfsvMBreuoRMZSZZy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:49:50"} {"_id": "9K4LjKYqWKzKp2diW", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\nall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "67KdRo5iX29twbB8c", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:28:56"} {"_id": "iNHvH4LjfaM24QEWT", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:15:25"} {"_id": "LQcPBTEA8hAj8F4pt", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "bymtPQKtZN7RzTuZb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:36:28"} {"_id": "A8SpRBG7ZHvqjNyHb", "cmd_c": true, "cmd_i": 4, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n, n1 : Node | n->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "QB4zzK5tuhkrhSNEi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:29"} {"_id": "2TTGDGmRHQCnN5Ahn", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node, a : n.adj | a->n in Node.adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qq2cemS99HDsHLtcj", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:42:37"} {"_id": "83GZ2K4kpEha8pME2", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tone adj + one ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bQZZt2ffBNzTZzk5C", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:15"} {"_id": "5AxeaH7bk4Rd745mL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x->y in adj iff y->x in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fRQrMeabNCYhRq9XK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 18:01:17"} {"_id": "ewYyLf4tni4T2kGbs", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "73GbJNnQokqwjqPmq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:27"} {"_id": "uxtd6vBHvH5wS59Hy", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 08:24:56"} {"_id": "k9W74KTfPeCkNm3gf", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node,b:Node | a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HY7ituoCXQpmhSTbR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:01"} {"_id": "k9xbwYnAMTtS7LX3v", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.~adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gmfDPqoqFg3DLaDnP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:40:17"} {"_id": "sSadCegAWG2Szusu6", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (~*adj).x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3AT3J4BH8BiwJgyza", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:17:31"} {"_id": "2LPr8TatJYLWJxSM8", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-9-17 11:52:25"} {"_id": "AB6Mm9aS9gvFGs4Q9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AN7d9YdhWvRaBSWz6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 13:33:09"} {"_id": "tdxhLj4DmvMMhwudW", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno ^adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MF5wp6YMqE9KzPoa5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:35:32"} {"_id": "oercZGuHgQRDSbaTa", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.~adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DgqzqwLH7wXBDFBA4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:31:59"} {"_id": "8CCNqNw84dj3sktgQ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "Subset operator is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-4 07:36:01"} {"_id": "3yvhg4GjefLGNzJEk", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "JrhoinguxnPh3rBpt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:36"} {"_id": "pLfRZSnHWjrvqhtLT", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node| some n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JTZBzLBZKbQzqrccp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-25 16:28:22"} {"_id": "zxdd25RcwmZSfrwSj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + ^adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "gyPjWbdvwhHnsfk47", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:12:12"} {"_id": "rSid3s7chaWt6QJSJ", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "wcFBKZuZkJbnZ7SMn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:33:30"} {"_id": "RnkHY3A2PMWf4azHf", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "9YCBJZujgdF7oduxR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:17:08"} {"_id": "MirTmyX4KtMiqDxLS", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wHLLFoPtfXXDi42Pc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:26:56"} {"_id": "gYF9E5GyDFjFxxHF9", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PrCWCPWQj68P96uTK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 10:58:29"} {"_id": "6ssqBggKApWe67Lsy", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + *adj.e1) + (e1.~*adj + ~*adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ywkC4zH8GF4NQZuMz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:27:52"} {"_id": "nB49BsZ95t7mMmfPm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "uxtd6vBHvH5wS59Hy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 08:25:01"} {"_id": "Qq2cemS99HDsHLtcj", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj->adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "u8z24tqzei93s4Ede", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node->this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:41:45"} {"_id": "6FdZPbFT43MeJ9qjH", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.*adj + y.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JKYRmpS7ePy6D4zfB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:56:32"} {"_id": "K3n3TNMHdYmLMJYDe", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall v : Node | Node in v.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall v1,v2,v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1->v3 in adj\n}", "derivationOf": "pHdCGb9Q4kWvYK8F7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:20:59"} {"_id": "i2tsnpJLTceLMuTf4", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.^adj+n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LPCKgE4yoaErHzZzF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:21:37"} {"_id": "XtqFBu5NZygPvBY5d", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "32iEyg6joWDg5aZPy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:22:36"} {"_id": "XyrLiWBL5zRwu8aoy", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tadj.adj in adj\n}", "derivationOf": "7w83DHLHtdzjhfWGJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:04"} {"_id": "hzWpr4tZ3uLZ8dgKz", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6Fez8sLoNMCA3LFkj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:19:05"} {"_id": "eaRf44rxdXkmeXkyv", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^b in adj implies b->a in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Yp6WzmcyjzTDWSMDy", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:49:10"} {"_id": "2XjfsDcLEGp4RhwK3", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : adj | ~n in Node.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jjh4pppDayqe4c44g", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:09:29"} {"_id": "KZKPFWpmN9oxRygNn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^(adj + ~adj) +n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ytjzvebLsLQnpMBzq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:33:33"} {"_id": "LuFp8vs9QrsC6R8qn", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1.adj.n2 and n3.adj.n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "eRqkxP3qxX9rzWcb8", "msg": "This cannot be a legal relational join where\nleft hand side is n1 . (this/Node <: adj) (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:06:32"} {"_id": "pHCRtSNTnGPSNcymc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:28:10"} {"_id": "YJtYy7XYM4ypr2SSQ", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj.\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "wT6nn7RnYMALZePeX", "msg": "There are 28 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:21:32"} {"_id": "LPCKgE4yoaErHzZzF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cJgBvQvwiXHRaKjwg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:20:49"} {"_id": "nZFuw9ijtZmK9zTbL", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n : Node | one n.adj and n.(~adj)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uQmSas6FoysfT5SLY", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:27:26"} {"_id": "qwYJZtweArAr2tdXo", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KRcqRcgHhwGWQC995", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:14:38"} {"_id": "97sQ2znaGZdrHH49h", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tadj not in ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "S3axTLgfc7eGnWZp9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:27:03"} {"_id": "MkfsJ5jMRhoJQuyzt", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fDJvS3Se98ebRAZFZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:48:56"} {"_id": "YNSYTHgqvKXDTwKsh", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6gu9tsuB5jRdKh3zt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:14:29"} {"_id": "LstGAyE57wwW8SMhq", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "hpcCN5WFWiHsiyFPD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:33:00"} {"_id": "HCJag2LRsbqmdP4XK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (~(*adj)).x \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nqtxa9mWXnBCb9hnY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:06:39"} {"_id": "Qs2fFKfE7htCc9gSB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj + ^~adj.n + n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BmzmTtYqWR9aCKYji", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:55:26"} {"_id": "gLN98Daky9TjK5t89", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n ~adj.adj in iden and iden in adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "efkY2hspDKufut8cR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 17:51:19"} {"_id": "FoJ4YhexBuNKErmgR", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | n.adj & (~adj).n = null\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JkRGeH5JR7hjubT4r", "msg": "The name \"null\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:06:53"} {"_id": "T3hMEGpLwgrNg7ANv", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uTtBRnAbhjydQzPra", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:51:33"} {"_id": "aTFXxGraCaL56cwyN", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qhNEZeGFFEM4QTBrc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:50:37"} {"_id": "DzYrs3Brj8KJN2Tes", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2 : Node| n1 in n2.adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "WSkPtuZ8jtCSXFDPP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:48:39"} {"_id": "ctwZMgL6HTyRWtLJo", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QJhGYQgFoTbSAd7vt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:52:46"} {"_id": "vdi85Zbw6kXKGza5b", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SR72x3NQQbbMAfJXo", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:44:20"} {"_id": "Kj6ZJmcfDpBoi9YgQ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + ^adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "sFncjzQJ3bszrDEFe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:02:07"} {"_id": "Yb7i5wbLrzLrmgGrZ", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rkgyStJFMxdqXhcWg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:30:27"} {"_id": "QxyEwdSYpTxSF2XXj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tiden in adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fFD6vhLWCMjCty9a3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-12 11:05:26"} {"_id": "HaJyneC6dW2N23coS", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in ^adj.Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kcuJ9aj2gxpuHFMmR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:35:21"} {"_id": "K6oui934YNasa7TQs", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cEkkWs55MBR5gcZBd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:58:22"} {"_id": "mjSqepcNqFaDCrF3b", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BYgRMEs2Qr45s38t2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:25:08"} {"_id": "bHmfmhZc4SYvTyN5o", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x.^(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "HprKC6MrST4Z6ARLG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:52:24"} {"_id": "xmJyGwpF9kyo4byDC", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (n1->n2 in adj & n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "5JwuLhbps6YiSjh92", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-16 03:41:36"} {"_id": "6QamdBATgY2rmSHi6", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5n6jaEbchxeGN2Yu4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:46"} {"_id": "nwDbFd5BnMzfiwjEv", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "cbNa2jzLbS8NmqqZZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:47:27"} {"_id": "J78k7z84nF5H7947y", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pHgxJZh8Fk6kNbrcv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:15:55"} {"_id": "LFa42FpdxJYvtz2FE", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^(x.adj).adj + ^adj.(adj.x) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8xcnh4pJbv3ySLbjq", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:50:17"} {"_id": "wKoirFWZgo72X3TMn", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2GPbPCksWsgdK2yuf", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 11:51:33"} {"_id": "K7kKmqBrA7kCS4EJu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | (Node - n) in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TqthQbJFSpEA7LGY5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:42:42"} {"_id": "FCNiHrsTDKnckzvaY", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj \n}", "derivationOf": "rt9ppwhyZYu3QHYsC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:08"} {"_id": "xjRj7RTXfqoh5QMEz", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "gyAHma6CCS7tJx3Fh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-19 10:17:46"} {"_id": "Hj42m8Z8aggGpjguB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "EMaYaBby2m6QJFJW8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:58:06"} {"_id": "RfzYheypgR2R2E6GG", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a: adj | -a not in ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kJXkP2xRrDtRLdqXD", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-8 22:39:32"} {"_id": "iZiNHLMJibWRorgB3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.^(~adj)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qprTRhnpbBwTbLHcr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:23:13"} {"_id": "Y6X5AZw5C6SfxXTqM", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj != ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yrBXRRCHD2qJAiPv8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:51:25"} {"_id": "4tD8tzHRZhi2XLTuY", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.*adj in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "zLKZaAjrqJ2WQwG7n", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {univ}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:34:59"} {"_id": "zCaWNj7XL657iddvR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj != ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XQS7ZFA7omAwE2BuQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:48:06"} {"_id": "yQstKD8HPgH5jYtrS", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | Node in n.(n->n.*adj)\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "hcXdMbWyXLkfzMftc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:39:36"} {"_id": "RsBW929b2qYogMZYZ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x & (^adj).y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w6cRf6mkyJkHFaDjB", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:11:28"} {"_id": "zLKZaAjrqJ2WQwG7n", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.*adj in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "7gvP8KWnAcAFEwWWz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:34:53"} {"_id": "NSnfyuq2kkzuJagCY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | (x in ^adj.y) and (y in ^adj.x)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "y98CC8tGQBhHuGkL2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:19:07"} {"_id": "P6qpZiQ35ggtQgLbM", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6eQnW6ge38zr6hxX3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:19:15"} {"_id": "wJg2qDShKsH7NbHGY", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n *adj in Node set -> set Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aGgEbJY2BXXPWjLp8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:00:54"} {"_id": "KQxRRkLEPA7CNFM7P", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | (a->b in adj and b->c in adj) implies a->c in adj\n}", "derivationOf": "7oZabXtp8g32zRgpo", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:37:27"} {"_id": "pX3p9YASC7N6yDTr9", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5bXgbwPKiFWAk4Gso", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:28:39"} {"_id": "9LrsYQzSekg5PPB3A", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tkwJrZ339qZerGfsF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 16:52:30"} {"_id": "5wbxzjRupchJhBuJD", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "9xfPhHKiKC8aT8pTS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:10:15"} {"_id": "55Ssa7ymvrmGBEAdy", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "o68MmhMCgwv2Rtizp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:19:46"} {"_id": "AApP2oAntWyAtmcDN", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KtMRpXiKqME5J5Ke5", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:36:25"} {"_id": "qAg3z5owryWxETJ2r", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oiGinmMY2JsWkGsaN", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:10:01"} {"_id": "JJDnJbq7MuNpRS8Js", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj.~adj & iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ka6aHwS5WggFiyXgm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:06:39"} {"_id": "WtGL7JAThmBDajHkP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aHD3aNG3pxnjpdizt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:53"} {"_id": "Fy6bxEx4P6CXhHY24", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node-n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SNv6qSJHXTFFgYgs9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:47:37"} {"_id": "ofALRJf4h9oygq7Qc", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8LougFCAqGFh8jnHP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:21:22"} {"_id": "5Mt7JGSySzww92QEu", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | n.adj = Node \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QeJuw3TDAxFhQnvnY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:45:17"} {"_id": "HFwTDHu2YYvqnY9tg", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.^adj\n}", "derivationOf": "8cm9R8hFwrbsXKpMB", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:55:14"} {"_id": "cbzqec2gZ4cA7FEj7", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | let n1 = n.adj.adj.Node | n->n1 in adj\n\n}", "derivationOf": "hY5mkiAcGWidRDSj9", "msg": "This expression failed to be typechecked line 71, column 23, filename=/tmp/alloy_heredoc8701774291349897635.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 22:58:36"} {"_id": "ziKMkjXhMeQa5QDqd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "i2tsnpJLTceLMuTf4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:21:56"} {"_id": "euZFNEk79gotubk2Y", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp:mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp:mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp:mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp:mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp:mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp:mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp:mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n \t^(adj + ~adj) \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp:mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n\n\n\n", "derivationOf": "PAdiBojtM99zHkrTe", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:18:20"} {"_id": "Tj8XXWAMNAC9jBJyY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in Node.adj + adj.Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ueGyL6TunATaKsi3v", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:43"} {"_id": "KGZLi3jguLdiNksCc", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t~adj implies no adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wzNTa64HseYcZoFfS", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:49:41"} {"_id": "Lm5C5MZ8F6WnRXNWi", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj+n\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "M88EMg5QBDD4qF57d", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 16:30:07"} {"_id": "AjviLmGTS2GDdAZXX", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MbZKoYdNoXbXow28i", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:50:47"} {"_id": "L8A3xJbAJ5gCG3ZLs", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mb6GodJWAHtjg3iot", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:19:15"} {"_id": "pkfBoSwS8S6ZqwvEd", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vgeMnJqZ2orM3dTXF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:14:33"} {"_id": "zBNM5gXPyXJRc2DHr", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nXtJrkmwFfzitCQ6B", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:07:42"} {"_id": "fe8CKvsgqixD69uKc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tGzussbXAWj37Bszf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-12 19:30:56"} {"_id": "dgJ5dgb3mofywz4sX", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9avngaBWLcTGqqsJZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:47:14"} {"_id": "pqTmZ9G7CZDrcbdsF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | some n->n.*adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "mc92eWCC5u2xu2e7m", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:39:12"} {"_id": "YJbEv33TSHQq6wcmM", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:27:20"} {"_id": "wf8ybW4cG8L5f4RDd", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SXCFi6jE8fccmpKzQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:21:37"} {"_id": "WzKL5ApSTw8xRbPgg", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "94k7j7T9tHG897EwT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:06"} {"_id": "pc5mBbjt8Trp9k3SN", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GWzJaCnL7DZmq3KND", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:20:49"} {"_id": "5nXcPFWDuNdtewziD", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "PGgtBR5rRRigJZydo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:57:06"} {"_id": "bADKLYN3axm6K7S9D", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "5nXcPFWDuNdtewziD", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:58:19"} {"_id": "rvZBeMYAxx7gMT7DK", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "ayd6NMHctmx46aw2P", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:43"} {"_id": "2f88wrQvrogKamQua", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "rvZBeMYAxx7gMT7DK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:45"} {"_id": "RBSDs8AQgraA3eddH", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9ENYHKQoAt2oHzsqC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:31:55"} {"_id": "9kJTtiAnkpFGXgSwy", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1, n2 : Node | n1 ->n2 implies n2 -> n1\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ffHvbfZZ2mFgca4SY", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:15"} {"_id": "tMkF9C5XqtrcYgi97", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall a,b:Node | a->b in adj implies b->a not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PRryy2jFvmhL9mTy7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:13:04"} {"_id": "9xfPhHKiKC8aT8pTS", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall a,b : Node | a->b in adj\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "gusmsvuZH7dSvqWN4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:10:11"} {"_id": "YtD3cDkTQSmKamQnn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node | n in n.adj.~adj\n\n\n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hfSih24aZjcmkPMXL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:16:53"} {"_id": "e6SsAFnMJbzg6wprY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bx5ucHXWpaY63PGrE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:13:46"} {"_id": "LyrP3iLXNNzAy34nQ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "DPquTShRiraDHbqic", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 19:06:20"} {"_id": "ydzparX5q7KQvEMXw", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Gcdq8LaLo2JdeNFYq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:40:46"} {"_id": "C4wJu9Kz9suLRH7Ep", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.*adj & y.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fERsYAH7pdxS6FZ5p", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:57:20"} {"_id": "ZK9fXZxsdq37CohPM", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KcHQxujFCpkJ7XPSw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:43:55"} {"_id": "ZNczwQrYXGdquPLj5", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = (Node - n)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6uYkyPjLoE8cZXSo5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:41:33"} {"_id": "cwkauwB7FLv7y3XZS", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj and no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vPqWxDQFhcYrvHdwd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:26:54"} {"_id": "5bSvvW572hmGWCPir", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5Nw9mFdi696ygvjD9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:45:04"} {"_id": "Xj5Hty5ikmwcJDDsY", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Kjsji8md2wuRJRSc4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 23:05:21"} {"_id": "ZtA4Q7GE4ND7hqzG9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj & iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "L4rafcZgLz66MbEmj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:16:53"} {"_id": "oBW9mZSxHC5d4p4L7", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a,b:Node | b in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "B6pLpfe92MMiDCkuZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:34:57"} {"_id": "eyAfGvKE32ps5kyov", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ypJiWXCAhifCPFJNq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:02:17"} {"_id": "gyPjWbdvwhHnsfk47", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "YyWyauYTtTm4GDrma", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:11:34"} {"_id": "7gvP8KWnAcAFEwWWz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode.^adj in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "DE5BkQXerKFiFWFAt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:34:20"} {"_id": "Ak3pB7yEZ5SGGvMQB", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1 : Node| n1 in n1.adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "859QMqHRS2tNijR5Y", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:49:10"} {"_id": "M5KDoZKgRxZfWSzwH", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies no n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JmkP3nGZoNgzGMHCy", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-13 17:08:09"} {"_id": "RxG6q6qfMs5X9shvx", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj implies a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7yLuH8kpFZN47uDqz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:37:43"} {"_id": "44EhcGvAKc5ciZGvt", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "Wa7EfaF2zg2A3xDQD", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 444, "y": 265.3333333333333}, "Node1": {"x": 296, "y": 132.66666666666666}, "Node2": {"x": 592, "y": 132.66666666666666}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-11-11 15:29:37"} {"_id": "ySfHpJqby5XLoDC6K", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "728YPFujpjZaL7KXp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 18:51:12"} {"_id": "eDeq4PwotqfKhTubi", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n->n not in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bmCuNM2yzXW8ScPo7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:08:32"} {"_id": "a5toEyRijrAFQdLEG", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NzcvWwu5ysdRR5n2Y", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:12:53"} {"_id": "Xjji5QmJSvQ37mkcE", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n : Node | n.adj.adj = n.adj\n}", "derivationOf": "WTZSNskZBgpb4Pzqp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:53"} {"_id": "RY364yS7j5S78Dtzm", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "p3kqYJqL7yN3FGrE9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:57"} {"_id": "hfSih24aZjcmkPMXL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node | n in n.adj.~adj\n\n\n\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Etb7DTZG8a8SKs26o", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:06:51"} {"_id": "Htir3qPFatNzqv9X8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.*adj + *adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "9Pt9srNPrCK4cLgb6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:27:55"} {"_id": "mqvMECHf4autQfW3o", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "K9YHtSbscdvfbDxY7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 14:58:25"} {"_id": "oF7nFAgMDeTK8dCJ6", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "D69NHhgXTn4XMA4Gu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 02:30:39"} {"_id": "LHkknDMqWdbb5Pgc2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eSsF5k3NaePkgrmSu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:50:14"} {"_id": "pTF7YrJeEuqipEK2P", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "7yYY363aDtpbcZFgv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:53"} {"_id": "TMC96HEiCuLsztpy9", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ywGH9ATwfP3MjZSNL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:47:29"} {"_id": "L6TxKmJ6WJqTDcbWa", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "SwdLhTyEaWH2tmPg6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 19:05:03"} {"_id": "p5x2pAWAge8ieP6J2", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node.^adj + Node.~^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qq7tLeBRzLg6svbxB", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:57:48"} {"_id": "Ba7yDTkS3TxH3uY5D", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in (n.^adj + ^adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xXA4QvEF2bfA5DR9z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:31:27"} {"_id": "tkB5XvCZ5GfSsasdg", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj implies not v1->v1 in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uGG2YYaL2QWNCw4fz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:19"} {"_id": "wvc8s6bLfBHiDxFAP", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | b in a.^adj and b in a.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "cSN9am85pguHERF95", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:03:15"} {"_id": "vx8kyBmmMm6mHgutd", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "7PzFmHBYRa8eBE4PE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:46:55"} {"_id": "cXMpcWcKR3oBnq85b", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a : Node | no (a.^adj & ^adj.a)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7Wft8kg9xfbeuAsxD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:45:17"} {"_id": "Yp6WzmcyjzTDWSMDy", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "98nWXmKKmoouseMnx", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:48:58"} {"_id": "7nx7Le6ReWTpREocX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^adj & n.^~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YkszeZJCQaWGe2pff", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:18:46"} {"_id": "G4Y8Yv8dPphdBCBPa", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "E5uib7rCi8a3pmyXu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:25:35"} {"_id": "nLStFi4vux6DTYsQ3", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj in adj.adj\n}", "derivationOf": "3KqtshyXcyf2n9Bn4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:37:56"} {"_id": "GcZA94r9cipP6g27a", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.(~adj + adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yzcYiZTmkvZ7z7zyn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-7 12:26:47"} {"_id": "DYYPcFxqQ9Hx3oMwf", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in null\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FhkQdwvv3SyEQeSkM", "msg": "The name \"null\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:05:44"} {"_id": "uoRLnqg4ZR9reYYYZ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j7wgY9vGYXJYQukMA", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:30:08"} {"_id": "txRjaXAQNJxoegEP9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node| a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7oSSmnDYCFLybjHtb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:26:10"} {"_id": "Sg5KfhFHHuzmfecxd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj and (some adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "GuksJrnzXs9wMFCan", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:34:17"} {"_id": "YeXjYHXEh8ugePr7H", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fRG2qTaKQMQwmWxB9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:25:16"} {"_id": "TKjnZpxzXQXdZKCN2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^adj = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "2o5B22RhTX9YCbD8K", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:26:00"} {"_id": "PWsnhr5LEDhPd92zu", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BhnwarbHBnkj77Jef", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:28:01"} {"_id": "AN7d9YdhWvRaBSWz6", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n no iden & ^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "stoQktpRdp2PCwdRS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 13:31:32"} {"_id": "aEqZ7hEHWW3zRK7an", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | n.adj not in adj.n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8CYPoPfwKjJgKFeBR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:14:54"} {"_id": "Yxfimmjb4f8pwwi2G", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj + n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hNKTTZF7NX6J4ms9u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:48:01"} {"_id": "rbsrSDycndWfoLQa4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "oKR5MqctGpZXZwy76", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:52:40"} {"_id": "GgvnkhBkbu94gsmfr", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node, c:Node | a->b in adj & b->c in adj implies a->c in adj\n}", "derivationOf": "hpFS5fcbXMecqkakp", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:36:31"} {"_id": "TdrRYfLM3AHuoK9NT", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall v : Node | no v.~adj + v\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gcoHN2n6KxBqD6bP5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:54"} {"_id": "ZnpbzFDd4ZtvTLJg9", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:01"} {"_id": "8nQJAsGJKN4m66qhx", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CbbjnxmTS5LAeZLMF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 23:04:30"} {"_id": "izQ4YGqfxiPE2r7vd", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tsome adj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WDivSjAWZSjQj9kFj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:27"} {"_id": "opXv3KycneLwNSvCp", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in (Node.adj & adj.Node )\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "iGXoL2tFLaymLQcfG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:30:37"} {"_id": "M8dtKELPQpQhNkdti", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n not in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MQEzCTtRWxH9nAhjP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 18:57:23"} {"_id": "g2errPZgcF2Fw7pWm", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *(~adj).x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "erEqGzBXKHTYwNMZX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:30:07"} {"_id": "3FqDiJTLs6RWayKbt", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.adj + adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "6ig9sdDGvMtcQTyej", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:26:20"} {"_id": "NpxCfq3PeouMH7zxh", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some (^adj).n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "upnNKoEYLqvFSanqm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:26:08"} {"_id": "Crt9T8e8cSWJXs8iz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *adj + *(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "aqdAaDe5pBwGkD8ue", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:24:00"} {"_id": "pXWWtLsQfRNe75evo", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5Fc23AsRfwMscyFPv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:00:30"} {"_id": "7TkTfM8p8ML6Li63B", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:15:05"} {"_id": "di7q7mjgyhN4PnQQp", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t^(ajd + ~adj) = (Node -> Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "E2hDiGQjvMhX8Xxba", "msg": "The name \"ajd\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:27:01"} {"_id": "3NYoc8CZYTSWcfLGr", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9ky3ZgNdPskrrpPs5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:25"} {"_id": "FhW6YGCuNbtoCvYZ9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ou3gPW2mHPJQzS6mw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:04:44"} {"_id": "CgyEnyqa9TdQ6L5ff", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:32:38"} {"_id": "zLzFDmnFDMfBH5EJ2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "CmPbQMPg4xWpGfT8u", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:37:21"} {"_id": "yd6u8QnwgsKCEQdwX", "cmd_c": true, "cmd_i": 4, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node - iden \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\nrun {noLoops} for 5", "derivationOf": "QNc7as2cjg32YCRco", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:19"} {"_id": "bY5gCvYEiAuWDgdch", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "XbCEGLStzAXbgaGZf", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-21 10:33:03"} {"_id": "Ewvvq5YBxdeyHXJSf", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(adj + ~adj) in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "EFTjANp3jDKA4ajyr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:34:48"} {"_id": "ciKA9Xc8D6vF39Tyx", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "4tD8tzHRZhi2XLTuY", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:36:23"} {"_id": "SoYveY2ns66b463wm", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + ^adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tall e1, e3 : Node | e1.*adj in e1.adj \n}", "derivationOf": "qwXXZXrCCqRSWByud", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:24"} {"_id": "ARwjpde9BDQEmGQuJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "o4hHApmqyEkBQPN3r", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:17:30"} {"_id": "Evcdue9hsrN3PLScy", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3Bg8TdnqmPaXE2tFk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:45:44"} {"_id": "h8ErKMkLSwWDXpfPG", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "43MbLspQCmiEdhyhF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 11:14:32"} {"_id": "G4zqwMfokBPLALTn4", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rZDktbWsFujggPKnm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:19:16"} {"_id": "HoErSgZybWu3QBQpn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "nnziX54a5XwEzGurb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 12:20:22"} {"_id": "sHih4z5BbsgN98pd7", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = *adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ynHWP2X54StuuzL4W", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:58:57"} {"_id": "HSJfPA8MH4EPfqcZD", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tadj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "7rZxXeQQYFwPr8uT4", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:14:22"} {"_id": "XF4RQJhpSmrbdL2vX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x,y:Node | x->y in adj implies y->x in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3FnHLkAd2iMsa8Mua", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:10:27"} {"_id": "KgJXFQSfEHd9GE5oR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "nxtvAf8yXraoi2fke", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:37"} {"_id": "6yJgP9tWfingkgcPD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^adj + n.^~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Sbf5KkhBTYwKKCk8k", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:05"} {"_id": "qZMPezGLD7BiDtZ5m", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \n \n \tall n:Node | Node in n.(n->(n.*adj + n.^~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "HFzw8Qd8QHmj9qJrw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 12:06:04"} {"_id": "aW4zrRosHLrKr2CuZ", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n none adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gf9T5hDj9WKjCxfAf", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{none}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:52:04"} {"_id": "8wPf2MEKg7NdXTH6g", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Qv8FuQjbomExCM67g", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:40:21"} {"_id": "fAexkNj8yrDiMJQG8", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in ^((x.adj).adj) + ^(adj.(adj.x)) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LFa42FpdxJYvtz2FE", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 18:50:36"} {"_id": "dASZeA6BADRBxwJjq", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "RK9yaQbZYpG72AH8W", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 02:16:54"} {"_id": "eGuCrt7jFLzsrdAp6", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tone Node.Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jaWh8KA6Dun9iazQ8", "msg": "This cannot be a legal relational join where\nleft hand side is this/Node (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-4 07:37:02"} {"_id": "PAdiBojtM99zHkrTe", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp:mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp:mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp:mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp:mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp:mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp:mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp:mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n \t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp:mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n\n\n\n", "derivationOf": "S4L4nGB2x8u56NTQW", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:18:10"} {"_id": "Ps7syFqzFjT3NpnFo", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bHKZE9tJgyrgAmjhk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 11:08:38"} {"_id": "NdPEcYSk7iL6B5cQC", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "awA5T6ZL5fZiNN3cr", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:01:57"} {"_id": "pPcgXFrMhPBaXkZ3g", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zCaWNj7XL657iddvR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 04:48:58"} {"_id": "q6RdnBX3g4wje58Db", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node |Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n \t\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj\n}", "derivationOf": "P36moBsWcYzdtXeMo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 13:48:04"} {"_id": "PRryy2jFvmhL9mTy7", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LsjBTyBkXuRkkLsvj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:12:04"} {"_id": "aMaRMPmYjYjXW2Zsa", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some n:Node | Node in n.*adj \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "X45LdbnEpMn24KuPR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:56:55"} {"_id": "tz9aPBRES7goqF5Qg", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (some adj) & (Node = (n.^adj + n.^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | (some adj) & (Node = (n.^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "ccwJei47u23WTaWAv", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:49:50"} {"_id": "Sa2cxPrzANrSRLqBo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n in Node.adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Mde7E2rPj9bdvDtCp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:59:23"} {"_id": "qZrWP2WLA2SsfMcxm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bkvcJ4LARF3Py3hQH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:49:31"} {"_id": "jMgDSNk3CfNFx6rv9", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 in adj implies v1 = v3\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8zBm5ujTgJcCHDacz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:21:45"} {"_id": "kzAjbi57Gqa9KjbvN", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | (n1->n2 in adj) and (n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "eRWhutt7jsN9zFQPj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 19:02:39"} {"_id": "xBtdzTScDwR5NRn5N", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Bn3r6qQ7T2CJwrZNo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:49:23"} {"_id": "ghsagQofBFoG5RDDd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RPLagYXAg54KSZph8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 10:39:47"} {"_id": "5reWhGQMDSRmKxpMY", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hPNSddghsyMp5kYh7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:36:40"} {"_id": "g95DWsmuAQygLjLJQ", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "m4gKLbomsu7LNPgBp", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:50:24"} {"_id": "27WiikEN3k65D2PzH", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(~adj +adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj \n}", "derivationOf": "dzJyQSGR5s5FQcEtd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 12:30:12"} {"_id": "LtBCGBkJ4AYHrXWpw", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "FbFzdbLaHfHkmkEMn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:34:12"} {"_id": "BM88cwyneH25nvP2H", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5bSvvW572hmGWCPir", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:46:18"} {"_id": "kw96r3TQJA6i2kBu7", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "zLzFDmnFDMfBH5EJ2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:38:05"} {"_id": "hpcCN5WFWiHsiyFPD", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "J6LwfcjGNQain3oEo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 22:32:04"} {"_id": "fERsYAH7pdxS6FZ5p", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x.^adj & y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "K3TtfSyupA3XH672Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:57:12"} {"_id": "vgvhjX2rFd32takzZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-7 18:57:00"} {"_id": "biNBpSd9d9omDN27p", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | b in a.^adj and a in b.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "9wv2dFGTAsivD6aZJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:02:04"} {"_id": "AEo9kSwvd4u6L6kSr", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1.n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | some ((n1.^adj).n2)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "GxaZaANgaJy7sAdgr", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:52:52"} {"_id": "SGYo7PebcuphJJ75a", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj - iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vQuftdrL93TQLrAQt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:24:19"} {"_id": "2jtgE9EzygZHm8CxN", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.ajd \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kXEDSxAW4AvRScZBa", "msg": "The name \"ajd\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:26:30"} {"_id": "hqeFGniFikj8EMscG", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZnpbzFDd4ZtvTLJg9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:13"} {"_id": "S6zmfRAAWNdDH9gK4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aGiod3ywisoNEbfj3", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:28:19"} {"_id": "xiCPsfJJuPpkteSpH", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | Node in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RBSDs8AQgraA3eddH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:32:20"} {"_id": "yYJtRJZqFpTWRDBmz", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\t\n \tall n:Node | n.adj or adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hmgbtfrgfmiHK9C2f", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:05:30"} {"_id": "ZD8HSoi93mN7rzaSR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t(Node.adj->adj.Node) in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 08:57:42"} {"_id": "728YPFujpjZaL7KXp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 18:50:40"} {"_id": "2gwGpcoMLLvAonzpL", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | no adj.n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BjHxAfy2eubvQi6DR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:37:06"} {"_id": "GWRKcsM85jkgSse4a", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6796CLjQdwhNhCZ6p", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:54:36"} {"_id": "nnziX54a5XwEzGurb", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in(all n:Node | some n.adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "7KetZH8HjryX2Cn5w", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 12:20:05"} {"_id": "mXvEaipP9ptRxF95R", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n +adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vT3aJKWMXcyBRxhPy", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:50:24"} {"_id": "Dif6vFzczyuPEvmPE", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "zeGiZa77FSzvwBy4E", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:21"} {"_id": "kFAgaLyzKiHc2hRJa", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tNode->Node - iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5ECPgxkWBXYYjFNKh", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:47:29"} {"_id": "u6Nybtof7zbcX57vj", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*adj + *adj.n\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "EwQCvoYcDrX2priKq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:08:58"} {"_id": "48mbTuPRH7SSe3Ndp", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G9oM82emj5bYFW3wa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:28:35"} {"_id": "tC6Bd294n5D99DMcC", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.(*adj + *~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "GwGTvsFJAGesBwTbG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:44:17"} {"_id": "fS3oRuNafFfKtm2EL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dtyMydKR8wjRe6aEj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 15:14:09"} {"_id": "c3m5YSWr8myhnoJEF", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PWsnhr5LEDhPd92zu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:28:04"} {"_id": "cwWwWG7Cms3e6P8EF", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in Node.adj\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2BQziERmhubJiWgxA", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:33:12"} {"_id": "sNab5R3TRADMgZCAC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P4CHHp2SXTAkNYQgW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:13:51"} {"_id": "TWQq2qmmjWeQPRK9R", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fKsMkPgb6YQwHT8fu", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:27:55"} {"_id": "6Fez8sLoNMCA3LFkj", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n != n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jDis82RxLXRohxqKw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:18:51"} {"_id": "W9W62iKEBpcD5FnxB", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:00"} {"_id": "j7yZ7deQRuiNJhg5d", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj\n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Lm5C5MZ8F6WnRXNWi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:30:18"} {"_id": "fFjvWNYLboWiA7m52", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SXabMHeCFnComme44", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 14:04:02"} {"_id": "859QMqHRS2tNijR5Y", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2 : Node| n1 in n1.adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "DzYrs3Brj8KJN2Tes", "msg": "This variable is unused.", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:49:05"} {"_id": "FACfvxnynK2Wtjr9q", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | x->y in adj implies y->x not in adj and ode in x.^adj + x + ^adj.x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "zxdd25RcwmZSfrwSj", "msg": "The name \"ode\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:17:02"} {"_id": "vTMfggpivgw9Cuo2S", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2WsGcFN36rtrEH89i", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:24:10"} {"_id": "3waQ5SEc4nnc9tHaj", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in Node.adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NWgfpJsNKdLsWAa5B", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {univ->univ}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:33:55"} {"_id": "TthbENRLPrbQRKyPi", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1, n2: Node | no n1->n2->n1 in Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "Zc8gCRAdSjMA8S5Ph", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:50:55"} {"_id": "8NSgbgbbhb8ZCc7AP", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "KQxRRkLEPA7CNFM7P", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 523.9921875, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:44:33"} {"_id": "eSsF5k3NaePkgrmSu", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w3QTiGJXCTM769eMe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:50:03"} {"_id": "vQhvMRD9uhZyx5xPK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Evcdue9hsrN3PLScy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:45:55"} {"_id": "seMsdesJDd8RS74N8", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | some n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bFqtA7DL6J8vD2sGZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:15:57"} {"_id": "gMPY6CRYXvKCwi8bo", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GJMNm7FBT7apbHCFh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:03:24"} {"_id": "ou3gPW2mHPJQzS6mw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FQzauHWBkTTkFFJXY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:04:13"} {"_id": "7pxdwusxoz7FoP5ak", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WX92g9i6ztzuWqX9Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:08:02"} {"_id": "tkqyY4cPSxJd7b6oi", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "bZDpu99i2QXmsPpvs", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:46"} {"_id": "Dssd4gqvbnWTXwMnw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "c5uxYBLzL7tPdfoZm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 20:09:59"} {"_id": "6eQnW6ge38zr6hxX3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode in Node.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "q9tG7cQSPXe6K6uTt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:18:14"} {"_id": "AeP4BqmC9ZyC35oaw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8ZR9ooeEapN4Mon9W", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:30:18"} {"_id": "JbhZZ5xL2Sm3vaP3S", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "u3iEef6ivSrfGyv5K", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node0": {"x": 328.21875, "y": 199}, "Node1": {"x": 656.4375, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-12-3 11:27:47"} {"_id": "osMzw7WMMrQ2tdhob", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj = ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RTAobn7tMhyajmWoW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:12:30"} {"_id": "wpTNxFqjs5KP78Pdg", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "QauacChiRXCxBirFw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:31:17"} {"_id": "jGR5o89Qh42dH3ZkE", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in ^(a.adj + a.~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BiefHMJdGbDGoA35h", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:04:52"} {"_id": "jRryt5ZmRaGGk63cD", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1, e2 : Node | e2 in e1.*adj or e2 in *adj.e1 \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bgL4a7RyRonDDrLWr", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:22:13"} {"_id": "67KdRo5iX29twbB8c", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\nall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "nDoXEb2GTXYTbRxKv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:28:52"} {"_id": "abtoGgqxkR7HvzLHt", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n none adj && ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aW4zrRosHLrKr2CuZ", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{none}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:52:12"} {"_id": "jLperDbhw7gY5H3p9", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ujT3HWaWkpBZBvX9B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:35:39"} {"_id": "G7dxsqa5FybTy3N4h", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "bB7B4PegHxwWbwP7G", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 12:00:51"} {"_id": "qqQuxqdWg7CCvr4qe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n->n.^adj in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "8a3WGNMxhGS9MBDFC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 02:36:08"} {"_id": "B8WWL5CtD46jbDPa3", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yyaQ24NMcJ2DnnCa9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 22:52:36"} {"_id": "zbMEQKnGQ9dGrtJmt", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "c3m5YSWr8myhnoJEF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 11:28:07"} {"_id": "zBqPXRijRo2my3viA", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DdQ4k2Gk4kcxBhr9c", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 03:32:11"} {"_id": "tFNbCLA8MiKarMXm7", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vx7ZtmK3CkDuFezNb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:47:36"} {"_id": "3HhsXXEdQHK4rNucj", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n,nn : Node | nn in n.adj.adj implies nn in n.adj \n}", "derivationOf": "JPWgRMRsKjArpYmQ8", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 523.9921875, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-1-8 20:01:43"} {"_id": "R3fzT34Eabz4aCBbj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "57C9SprMF7NfxTZAm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 15:43:10"} {"_id": "6gaKTBD2zKqFHj75T", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "dL52xdkmhFyyGf9sJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:39:52"} {"_id": "o47ouLtwZEW7bskG5", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wEnprghN5RwTT33iT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:07:37"} {"_id": "dL52xdkmhFyyGf9sJ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode = Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "Xqv8zkd8g24ZDtFzc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:39:10"} {"_id": "WPza5ZntBDANXSEXA", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in Node.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xy8aKzRyYTHzucfGm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:41:09"} {"_id": "LdWP2dDAsG4XG23Rz", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n->(n.^adj + n.^~adj + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "SdHweCDuCZsd546eA", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 11:57:10"} {"_id": "tCByNmgELfNEkunCX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in ((e1.^adj + ^adj.e1) - e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HTX3LDQoCcmzwjAax", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:25:59"} {"_id": "dBwZS5CQy6Ycduk4h", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FtdSvo7WmeWnmcJsZ", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:33:26"} {"_id": "9ENYHKQoAt2oHzsqC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qjA847HaNscTxCzDn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 22:31:20"} {"_id": "HzgA5ju3QfGt6iXXX", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uzkJJdBg7rqESLcRS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:11"} {"_id": "9YCBJZujgdF7oduxR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:17:05"} {"_id": "7kHX8LJmhrMQx27qW", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node and some n1.adj:>n1\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "KwoukwPdoDrSeBtfK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:30:21"} {"_id": "4wZ6uc3zLpGEcZSSH", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "6gaKTBD2zKqFHj75T", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 22:43:45"} {"_id": "6GM5o3oWPQm43e2kp", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no adj & ~adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "utuLRrX37FjrXFJ3k", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:29:05"} {"_id": "nvvfESNDHkwibFcMj", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QNyLcridNnahyXvC5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:00:28"} {"_id": "72tEMMBhxCi3EY6Qu", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | some n & n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wwAsZiim4hmxSeXe8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:18:42"} {"_id": "WHunptE7RoLYc2aYR", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "txRjaXAQNJxoegEP9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:27:03"} {"_id": "jbYNyAG3c7Pt5Etn7", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "M8dtKELPQpQhNkdti", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 18:57:32"} {"_id": "mvnEKm76bCQXeRWo2", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:15:53"} {"_id": "ehxTCGuathmCdTP9C", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-10-28 09:09:41"} {"_id": "NTKcueytcQtwhNjJt", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies (b->a and a->a) not in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hEAzduJktqR8k95Kj", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:15:30"} {"_id": "zTWzN39t7RqEMNozw", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KrYCZmzMR9XNYeixR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 22:45:24"} {"_id": "5xZ69DdKrq9JweJMp", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n != n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ZtA4Q7GE4ND7hqzG9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:17:08"} {"_id": "k3sThKCRBKBeo87Wg", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node, c:Node | (a->b in adj && b->c in adj) implies a->c in adj\n}", "derivationOf": "zG7xmzrR6ysFKcm6o", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 15:37:08"} {"_id": "LCGomNRQLJc92jw38", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tNode.^adj\n}", "derivationOf": "PQtMTsNnYXg9cpiHo", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 11:31:27"} {"_id": "eRL96wYnL6KqzRkgW", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\ta.^adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mqvMECHf4autQfW3o", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:01:05"} {"_id": "G4AfcvaxzZso5sC62", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tnull adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DYYPcFxqQ9Hx3oMwf", "msg": "The name \"null\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:06:02"} {"_id": "6AARkKMq8NAZTw9ov", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in ^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Xj5Hty5ikmwcJDDsY", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-26 23:05:49"} {"_id": "hCuAkL9LHnbbxWoEC", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KZKPFWpmN9oxRygNn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:33:44"} {"_id": "zvddRcbZ8QFYKDueg", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\t\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "MMtz5hFfvLqb4pBvv", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 12:09:06"} {"_id": "GmXYbPzHaNXzxPYju", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "nxtvAf8yXraoi2fke", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:19:40"} {"_id": "p3kqYJqL7yN3FGrE9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | n1 -> n2 in adj and n2 -> n3 in adj implies n1 -> n3 in adj\n}", "derivationOf": "pTF7YrJeEuqipEK2P", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:04:56"} {"_id": "Wa5cAQyt2BgFoz3fY", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:18:13"} {"_id": "Fv2tah6dPXTTz6eL3", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "DAhmNHdT4Ykjnd382", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 11:18:22"} {"_id": "KW2jgNyaWn6CYAsgB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TXo8dfXweDvXQQfPd", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-1 19:00:18"} {"_id": "RuKce7kjuwmEyhAwv", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | some n.adj && Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "eNtX4q7f7vuxzdtXQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:35:32"} {"_id": "7Sg3ePKWNe7ZFEDho", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tdxhLj4DmvMMhwudW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:35:46"} {"_id": "3FnHLkAd2iMsa8Mua", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x,y:Node | x->y in adj implies y->x in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JLskqLPYLqHGw7RMP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:09:06"} {"_id": "a6dY6NoT2av3RE4NW", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n: Node | n.adj.adj in n.adj\n \t\n}", "derivationOf": "gyTqsF6cx73CirwvE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:27"} {"_id": "kgmqMnWtuc3Xc99ZB", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "QHsiCvbQSxFCHqSBm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:32"} {"_id": "ireSmZCH6CbEop5um", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | all a : n.adj | n in a.adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HbvN8v4WceR2De7RC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:30:51"} {"_id": "twXaXTrAfArTDLgAH", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hCuAkL9LHnbbxWoEC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:34:18"} {"_id": "Y6sBCTtMJfokmSBXi", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tnull (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G4AfcvaxzZso5sC62", "msg": "The name \"null\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:06:33"} {"_id": "xCoMPxS9uCBPG9DBb", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AZpmKxyPwuRosGSaj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-26 22:32:31"} {"_id": "hNKTTZF7NX6J4ms9u", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tFNbCLA8MiKarMXm7", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:47:52"} {"_id": "iDzodpYPCjBkPv6XC", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:21"} {"_id": "52eDtwkrP8HxNQ2Hi", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "XQHyQnFr9mTMccT59", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:56"} {"_id": "xvmti93o94B2nsGYS", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 : Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1 : Node | n1 not in n1.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fkJ3kLAo8aEFnRPiE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:55:09"} {"_id": "KwNcKLC2ya2T4WARx", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n \n all n : Node | n != n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RAoqZ2ut3CTCTXoNN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:40:54"} {"_id": "QMFgZzjQCGNwcaWzJ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "rCTnnMzuy9wXq3LZi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 11:58:18"} {"_id": "6AGSK87R9Yso6DeZw", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n in adj\n\t all n : Node, n1 : n.adj | n in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all disj n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t all n: Node, n1 : n.adj | n not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t no (iden & ^adj)\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n2 : Node | some n1 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "XxddJhGvr9AEDfZoc", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:34:32"} {"_id": "Doco3ZyE8xP4iGz2r", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.adj & x\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G8D2c9cnobkghnioX", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:32:49"} {"_id": "P36moBsWcYzdtXeMo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node |Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "6h2er7TT3bYnJ46LW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 13:46:10"} {"_id": "2WsGcFN36rtrEH89i", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YpenAg9MZX4t7LcLo", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:00"} {"_id": "ASDgN3J7wW3MEvruE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.adj + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "Hj42m8Z8aggGpjguB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:59:14"} {"_id": "NMPohfgtSxE6Yf8s8", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = no Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sMa67yC6r3FuarjsP", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:38:15"} {"_id": "SzaiuGJAqoCX8FAni", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oik9A9zaeHAzv3pfG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:16:35"} {"_id": "riXQABo88KZvRbg6R", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n in Node.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tSxZBcRMQTMgs99yB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:37:19"} {"_id": "grgXKknv8TJMDYX7W", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.*adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jdA5L2cMb89HceY2J", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 16:59:09"} {"_id": "yGYnKyNKHeJ8jyuss", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n<:adj != adj:>n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8ukpyhd7qmdzuC3Bv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 01:48:35"} {"_id": "HRPnsvM3is7KvwTWS", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tNode.^adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ETn3sydhWzAEkXo3a", "msg": "!in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:04:52"} {"_id": "R4PcE9zf47D8CRirn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-10-22 10:28:00"} {"_id": "gjPdWokZk8eoDykhd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj and some adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "qrgvQp2h6kzDWQwgJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:11:56"} {"_id": "LKsufvh23LkXR4TX6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n in n.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HW36CsWuLpruSX4EG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:11:07"} {"_id": "xQfCa7YFgmpSNkgE3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall n1,n2 :Node | n1 in n2.^adj or n2 in n1.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "YQ9YAJwzfwdxwLQC8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:29:39"} {"_id": "mgdrMvgjeKhmPWMtF", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 20:35:19"} {"_id": "G3sokYvfL4JpBtXu4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n : Node | n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NyBS3zTba6BStrTRs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:37:23"} {"_id": "zeGiZa77FSzvwBy4E", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "\nsig Node {\n adj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x + x.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.^adj + x\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-4-16 18:31:16"} {"_id": "ZeSnFu9qNN9d66exK", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n,n1 : Node | n in n1.adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ouSfYNs9msZx565to", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 00:15:48"} {"_id": "87wpMu8MjoCd83XxN", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall disj n1,n2 :Node | n1 in n2.^adj or n2 in n1.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "xQfCa7YFgmpSNkgE3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:30:12"} {"_id": "vTvkRQGn9fgHWwuLH", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t all n : Node | some adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some adj.n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FKCf2nDBZE5qDX6Tz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:27:28"} {"_id": "aiJp8RfrXNxCuNsX6", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a : Node | a -> a in adj \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "x3jXpizFmwPrHjFzd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:44:05"} {"_id": "JAg7y2dd8qJtG9bEi", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node = n.^adj + n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "XGAa5RaQNfqAqdoo9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:45"} {"_id": "kapz5CR8jaADwoFPo", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tcomplete & oriented\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n\n\n", "derivationOf": "tur86Kb8rexN2NnjZ", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 15:17:04"} {"_id": "Trc6AxRHMQtTtCw9D", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "h8ErKMkLSwWDXpfPG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:14:50"} {"_id": "Qq7tLeBRzLg6svbxB", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node.^adj || Node.~^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iyeH4wFBisXJcP7dG", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:57:04"} {"_id": "5R98C8GC42ermSJ46", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YXDCQRkTr72i4xS4k", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:01:37"} {"_id": "zw5t9ThfDLgKbRNeL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CkqGwk3jtzCKDNxXL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:47:06"} {"_id": "qe2fBD59CHnE5CJkk", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall e1, e2 : Node | e1 -> e2 in Node implies e2 -> e1 in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:16:10"} {"_id": "tFXCLpfpaZ3Mewwkj", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | n.*adj in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "p2jqAZ5aCAkHLS2yJ", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {univ}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:00:39"} {"_id": "ZJ5ycZtXhA6jiArJn", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "2Kfs5Jr9fAhSFedEd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:40:32"} {"_id": "f7WkgKppQLvkXyXkD", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies no n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Jxo79wmTzrwGXxcwK", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 15:13:23"} {"_id": "MNwyNtTMJ3XnjnGLH", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\t\t\nall n : Node | n != n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aRvsj2MMR7DmkvSpR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:20:13"} {"_id": "eAFAwu4wu2R4B4zKA", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n \tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cuR899z6BnXzsNSQf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:41:48"} {"_id": "76BEedCwKhrbv8W8D", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj && undirected || one Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj || one Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "Tr6P6habsLAuqWEv6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:20:21"} {"_id": "gZNZxog3EnERE4vF7", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: None | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CiABZADLDvYdgKLTr", "msg": "The name \"None\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:35:12"} {"_id": "LMqrJsBfznRKFKDCM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zLJHAFysrxgGbCcqs", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:33:31"} {"_id": "SXabMHeCFnComme44", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "E3QoLfYrj8vgwfpHm", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 13:43:36"} {"_id": "Aq8MxyYK4XNwcd6Hf", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | Node in n.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xiCPsfJJuPpkteSpH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 22:32:31"} {"_id": "WQimqaMkMMkwN8vyy", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n, n1 : Node | n->n1 in adj => n1->n in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-6 00:55:01"} {"_id": "YZ7WD4sqAaMQThRLc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:37"} {"_id": "KgHxmwY4LTz5TCvKZ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NrcBn39i4HnqyP5i4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:22:16"} {"_id": "HPxeXwBMKnBRJZx8W", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | (some n.adj) && Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "RuKce7kjuwmEyhAwv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:35:50"} {"_id": "x3jXpizFmwPrHjFzd", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a : Node | a -> a \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jxwQWahqnjkGusz2B", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:43:58"} {"_id": "wHLLFoPtfXXDi42Pc", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "a2vqEGaHnm6Dn86Z9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:26:31"} {"_id": "JcJEiJ67rPLSht6oM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "X9EiLje9c6GhooJgH", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:32:38"} {"_id": "s4HncYwwCin8j7uGT", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n", "derivationOf": "cL77F8QNj95tjuEBq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 15:11:18"} {"_id": "92p7rpYXmdCjndDXB", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x, y : Node | x->y in adj implies y->x not in adj and Node in x.^adj + x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "6yLeXCu9pyDWgaw3y", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 19:18:32"} {"_id": "ms6XHLgopSxdw956B", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some (^adj).y & x \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RsBW929b2qYogMZYZ", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:11:49"} {"_id": "xqpuoBSRuwJiXZNgZ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t Node in Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RGnvREanCJiFyHdk8", "msg": "Subset operator is redundant, because the left and right expressions always have the same value.\nLeft type = {this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:22:13"} {"_id": "nTqqRkwWZsDh8BrC3", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n not iden in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fwFQfhPeGJXDPCAwM", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:57:38"} {"_id": "LZuQYDQ3CWhDkZmWi", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uFfxg4xfkm4psH25t", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:08:44"} {"_id": "rkgyStJFMxdqXhcWg", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj = iden\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "48mbTuPRH7SSe3Ndp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:28:51"} {"_id": "qofWKq8s9XJJK9sSB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.*adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "QMFgZzjQCGNwcaWzJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 11:58:45"} {"_id": "HprKC6MrST4Z6ARLG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.^adj + x.^(~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "KePxi2WNwz2aP5u3z", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:52:20"} {"_id": "8uRkKjAF5yhBHQAzn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "A3DfRnxryfc7pjzYA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:07:34"} {"_id": "PGgtBR5rRRigJZydo", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n Node.^adj\n}", "derivationOf": "24kzkZoATsJK2Jkbj", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:56:56"} {"_id": "ncQcEZon9gFgfsg2X", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj and y->x in adj implies y = x\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qFzsh8K7e6rCrZnvD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 17:55:02"} {"_id": "RGnvREanCJiFyHdk8", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj\tin Node \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xJQbYyFKkAEANZvne", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:20:41"} {"_id": "tZcdAJzCgbSFLMSnz", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^b in adj implies b->a in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and a->c in adj implies a->b in adj\n}", "derivationOf": "eaRf44rxdXkmeXkyv", "msg": "^ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:53:15"} {"_id": "hAqqKfjL8vgrjEwGq", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t(Node -> Node - iden) in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ocvo2sw4pJ2opccAT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:28:39"} {"_id": "kXEDSxAW4AvRScZBa", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "WcHG5rPwRm793sFiP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:17:44"} {"_id": "5JwuLhbps6YiSjh92", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (n1->n2 in adj & n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "SjHimjjmKqCLCPAHz", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-16 03:40:32"} {"_id": "GuksJrnzXs9wMFCan", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj and some adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "LstGAyE57wwW8SMhq", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:34:04"} {"_id": "5L2wPRwaZoEH6XNij", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some Node.adj and some Node.~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "wbfo9CFtoYm5BT58G", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 18:18:16"} {"_id": "pxu2xa7XFGKmRvDHF", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "mgBAEepxJoJFpAWqP", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-8 19:51:36"} {"_id": "cxXfBqPuxiEFCJ65x", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node| b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PCHukSp2SBqHQJNgw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 15:31:38"} {"_id": "fwFQfhPeGJXDPCAwM", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n->n not in ^adj\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Rjymaeqx75Ncix7mL", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 09:57:19"} {"_id": "4rJ6C5dg9CXtQxyTR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "F6wdXsHtG5F27sTEg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:17:23"} {"_id": "EAzkeFhgrkaWmB6eX", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6sRKNAiAScZJyPxMT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:16:46"} {"_id": "HPHSW5y26TePjjXGH", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n Node->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "k8E4Wzyq2y32ZE7xe", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:27:28"} {"_id": "wEnprghN5RwTT33iT", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b in a.adj -> a in b.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uGBozgPucQAsrAAFP", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:03:21"} {"_id": "Qv8FuQjbomExCM67g", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ghsagQofBFoG5RDDd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:40:03"} {"_id": "37o8miY3NLgMLmynJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1 in n2.^adj || n2 in n1.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1,n2:Node | n1 in n2.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "LGvqbFiKGiiiPnJT2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:01:06"} {"_id": "SNedL2rPSv3B53tzx", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JHz6oG93BMwgzpHrF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 11:06:51"} {"_id": "dAj9fuhg7eMwtbfDZ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.(^adj + ~adj)\n\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kRcXZck5gHaRWrQkn", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 17:57:20"} {"_id": "TKoWGrpZ5Rw8SuYX2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FF87Eez2YcHfgWdZ4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:27:43"} {"_id": "emDWrWp3hivTdGnSo", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n1, n2 :Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n : Node | n not in n.adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xCoMPxS9uCBPG9DBb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-26 22:32:38"} {"_id": "SJ3WGF6MLtaBNfifk", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t^adj = (Node -> Node - iden)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zwpftA6GRjPqWtRb9", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:55"} {"_id": "diF9tWF7dcSb6CEYv", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "44EhcGvAKc5ciZGvt", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:40"} {"_id": "utuLRrX37FjrXFJ3k", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YkPEWPwPKkKRsjSaa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:28:00"} {"_id": "dZQEh6PfskrfYvArB", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | some n.adj or some n.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1 : Node, some n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}", "derivationOf": "y5hk2Z8ArbPDPFRAn", "msg": "There are 8 possible tokens that can appear here:\nNAME disj exh part private seq this var", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:18:14"} {"_id": "9r6ncm6MBAKGpfCqx", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in Node \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uoRLnqg4ZR9reYYYZ", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:30:19"} {"_id": "eQo2woKMcZDg9JYZi", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1,n2,n3 : Node | (n1->n2 in adj) and (n2->n3 in adj) implies (n1->n3 in adj)\n}", "derivationOf": "kzAjbi57Gqa9KjbvN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:02:56"} {"_id": "aDaWgWe9R3hqLBGbk", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 & n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "AYbdXtQdaEsRRHnjX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:34:47"} {"_id": "XgMtjkHeQT9YTkoM6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Y4huvwtn8bjGD25D7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:16:09"} {"_id": "tW3vyhDt5cF6jCjfn", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj & n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "JSrKFvgKSAn2x6ZCT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 19:02:23"} {"_id": "XMgX7CbdJzQnY84qK", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.*adj + adj.*Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "xZHmaw7FJpKjsFhnt", "msg": "* can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 11:26:20"} {"_id": "CuushxHTdF63s7Emy", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \t\n \tall n:Node | Node in n.(n-> n.*adj) in adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "qMjgaYt67mxif8wHi", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 16:38:31"} {"_id": "KKY2Gg9nAsaeXayH6", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nno adj & iden}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "rfXa7BruPqMqgiTHy", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 11:13:24"} {"_id": "nDoXEb2GTXYTbRxKv", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "97sQ2znaGZdrHH49h", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:28:45"} {"_id": "xXA4QvEF2bfA5DR9z", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in (n.^adj + adj^.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G3s2yBNxWhoJTFnFC", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:31:17"} {"_id": "3yZRJAxM6XKEJFYwY", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tNode . adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hKh9tSHbyB8TQzBZZ", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:27:16"} {"_id": "aGiod3ywisoNEbfj3", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n\tadj not in adj.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BfzxXSYXC7xs6mgQw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:28:04"} {"_id": "wn7QpJo3GET8sTavR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj + ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zEWZC32rgdonuMxko", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:49:53"} {"_id": "oEqbfzmvcPZLQkQxb", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2n29Een8WGsMfpqZa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:01:44"} {"_id": "RNWm9rLAbNdf7HxBC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "e6SsAFnMJbzg6wprY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:14:18"} {"_id": "HAFmoKgKDjmhKAekB", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a : Node | a in a.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xR9sgNgL6Rk7cSAGR", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:36:26"} {"_id": "GTFdCpcZGq5w3XqC5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.^(adj + ~adj) in Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "XipvfopivmfLyFwJk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:35:35"} {"_id": "XR7aKcxN3PSuPDZ2p", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nNode.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "74BhGT5chxBWvvLZ3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:27:48"} {"_id": "cSJcZkF4HdP78CvHw", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~adj\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5EieyPXsbR8rCGAY2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:23:45"} {"_id": "TmF7SnJ23EnCoyxb8", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x in ^adj.y & y in ^adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "n9Y9NtbL5xz9kihpg", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:18:39"} {"_id": "MEP7NwKFuD2BBXnDg", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"a\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:46:15"} {"_id": "NcJKfevQJhgWbKpqC", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | ^(x->y) in adj implies ^(y->x) not in adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "E7gBkTkz6fLkmKHsj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:19:10"} {"_id": "xJQbYyFKkAEANZvne", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tno adj\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cxC7awE96zEcMjoSN", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:20:23"} {"_id": "SZeMz6Q2EEqMa88By", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.*(~adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cSJcZkF4HdP78CvHw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:23:55"} {"_id": "9cno6vejYomDELtcs", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno ^adj & iden\n\n\n \n \n\n \n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "x5v3RhfkZQjc9eEZP", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-2 23:23:09"} {"_id": "qS42e7GvgKMH6NpjB", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | n in adj.Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5reWhGQMDSRmKxpMY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:36:49"} {"_id": "gxFh5kqiaWu8v6bbL", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-6-20 14:20:59"} {"_id": "X45LdbnEpMn24KuPR", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some n:Node | Node in n.^adj \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "BRmexnNjDbauEbFpj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:56:39"} {"_id": "dAPKLnjtbfAqAQQDC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:31"} {"_id": "sab8zkCobCi2WcCTE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "aRR9xYXLap7dPzxh3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:41:56"} {"_id": "Cx49Qtkwk5DqojG7D", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n iden not in ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "T3hMEGpLwgrNg7ANv", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:53:03"} {"_id": "6PneyhSLzx8DXNcmG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in n.^adj or Node-n in n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "jXjSkKzdMu5RdYPR3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:11"} {"_id": "GNWpPGMyzZumCDrEB", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \t\t\n\nadj = ~adj }\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.adj}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \t\t\n\n \t\n\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \t\n\n \t\t\n\nall disj x,y : Node | x in y.^adj}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "nbeRopRNWx9QDt9Nn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 11:15:42"} {"_id": "NrcBn39i4HnqyP5i4", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node-n in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CHWgPv4rJYN2L2aRk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:22:02"} {"_id": "9rNbmi4J6yZNSzoGt", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2, v3 : Node | v1->v2 in adj and v2->v3 implies not v1 = v3\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vs4i3u8EG3BG7YmsW", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:21:31"} {"_id": "tEzCCcomXBSBJDt33", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node |Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj \n \t\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj\n}", "derivationOf": "rsqQiavx4XQCmMz6n", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 13:48:48"} {"_id": "K9YHtSbscdvfbDxY7", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tnot (~adj = adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pCvga24EkBnE8qjyX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:56:26"} {"_id": "AfwhyotybjQAbnmMK", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | adj not in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GTM9Zngquc4LaiJBP", "msg": "!in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-3 11:41:34"} {"_id": "GTM9Zngquc4LaiJBP", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "zbMEQKnGQ9dGrtJmt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 11:28:14"} {"_id": "gzCAqsvAbQo8ribSv", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2020-9-17 11:52:23"} {"_id": "xWuCQ9pFmfGGFtFWq", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | some n<:adj & n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2ZNrNbuwoNj2hExfT", "msg": "& can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:35:16"} {"_id": "Eq8XhpBARoF8gQmfL", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "RnkHY3A2PMWf4azHf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:17:38"} {"_id": "YM2pzGASNpwdBzyMv", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj in (^adj.n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3FYq4zrapSmAAezxs", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:14:52"} {"_id": "cvTe5vqm8QzhFD2GE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "3yvhg4GjefLGNzJEk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:17:37"} {"_id": "qBMqD2h3rhvu2j6ki", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in (Node.adj + adj.Node)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t \n\tNode in Node.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "HbZQ7z4SDyWGXSKvq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-9 11:17:17"} {"_id": "X2oxyfPbQxoRTzgh9", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t*adj in Node\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cwWwWG7Cms3e6P8EF", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:33:19"} {"_id": "bFyqE54myM775ZyXZ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:18:28"} {"_id": "MAcNBozp89qSFwRxf", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YPScjHeMPGASBn982", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:00:54"} {"_id": "6796CLjQdwhNhCZ6p", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tadj = ~iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iZKQQAS8TEEXJhh3z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:46:34"} {"_id": "usTK8xxodgCS5oxAk", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1: Node | not n1->n1 in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FYabHWaPYhcLHnY6A", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:25:09"} {"_id": "FhRC5ZhMSE9sRjHx3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:54:18"} {"_id": "ZvHxDKndqbLsnu2sL", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n Node.adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "h2opqd2XmxF98phTb", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:44:48"} {"_id": "jxwQWahqnjkGusz2B", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QTqswobtcE75gzwYC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:41:46"} {"_id": "Jv64FRe8ME4P8QqSJ", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + x.~(*adj)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eyS8GNH5uq2xanYhb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:33:07"} {"_id": "kxspMeeSdr48MN4z4", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\t\n \tadj.adj in adj\n}", "derivationOf": "XyrLiWBL5zRwu8aoy", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:45"} {"_id": "itgmEii7jRfo8DW2Y", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2qKHa3CPrD2W3QgJc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:17:32"} {"_id": "o8CZ94XxLryNKywRX", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "ehjdRJM4hGmm3SZGX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 19:01:12"} {"_id": "cb9QyomhJhKNxGCg8", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | n->n not in adj\n \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "FM8Rwcmb2GqAWGfme", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:54:12"} {"_id": "bvhxNxEvLzp3X3NQ9", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall a:Node, b:Node | b in a.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall a:Node , b:Node | b in a.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a:Node , b:Node, c:Node | a->b->c in adj implies a->c in adj\n}", "derivationOf": "8QKgPrG4fpDCvRXcA", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node->this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-18 15:36:00"} {"_id": "LnGrGqnjjki4F2Ls9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj + adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "c5jCqD5E4e3RP5APg", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:27:25"} {"_id": "gE2SthB546Q4a543H", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "xpf4gzd4yCSTGhWeo", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 18:46:24"} {"_id": "nhxssfvvPQdcGuuxG", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n3->n2 implies n1->n3 in adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tadj.^adj in adj\n}", "derivationOf": "froNtQRxCWe3JvMPq", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:11:47"} {"_id": "pCvga24EkBnE8qjyX", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (~adj = adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uqL8QWjEsidXDawCD", "msg": "This expression failed to be typechecked line 21, column 2, filename=/tmp/alloy_heredoc11149242233677729154.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-19 14:55:26"} {"_id": "MzeN2k4QEG8MiuDvd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n\tall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "xdHwrpN97tnsojeDL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 05:42:34"} {"_id": "QSMupbEutHnuaE9hg", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Ak9kEfZ4hKKEqXuEX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 16:41:15"} {"_id": "vT3aJKWMXcyBRxhPy", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n +adj not in id\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xBtdzTScDwR5NRn5N", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:50:15"} {"_id": "pshafKoidADvxFtDM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | (Node-n) in n.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "zczBFKsj9QFvS58SA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:55:52"} {"_id": "3ySsvPh3fXLL38YXY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node = (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "HPCEBSNYXz4iwL9bF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:42:31"} {"_id": "57C9SprMF7NfxTZAm", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1:n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bxH8etmD4mBordgn3", "msg": "There are 3 possible tokens that can appear here:\n, { |", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 15:43:03"} {"_id": "c4Jr3Pn4o2kzr4bKo", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2) and (n2->n3)) implies (n1->n3)\n}", "derivationOf": "HxTSxReiumnp9kkFE", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:05:08"} {"_id": "k8E4Wzyq2y32ZE7xe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8R2MnZcM2daPmbq2B", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-15 18:13:27"} {"_id": "BYz253ounAE6nRZR2", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cxbQWHBtNsqtGHHL8", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:37"} {"_id": "zKJB9aKBvBqKzGafy", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | Node in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | Node in n.^(adj + ~adj)\n\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n all n : Node | Node in n.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iZiNHLMJibWRorgB3", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 18:23:19"} {"_id": "PDdWyjL5zf4tPfjyb", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SZeMz6Q2EEqMa88By", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 21:28:54"} {"_id": "2khwuKcYMQkmn34bH", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vzuMpX3aAWpHYJJSB", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:29:20"} {"_id": "mgBAEepxJoJFpAWqP", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "8NSgbgbbhb8ZCc7AP", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-8 19:51:07"} {"_id": "NyBS3zTba6BStrTRs", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "7FWhprWJmqF3vn2kT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-3 09:36:26"} {"_id": "N5Qy6qw7RnB3HdNnx", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | ^adj<:x in ^adj<:y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tmuJLQNccZMpjdcah", "msg": "This must be a unary set, but instead it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:17:08"} {"_id": "CSK8qoy3fsWBfwYx6", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node |Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "P6qpZiQ35ggtQgLbM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:19:30"} {"_id": "5wJ9iBbsBY3DqoyWH", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tall adj.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "a5toEyRijrAFQdLEG", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:13:03"} {"_id": "PCQZGyFgAGFEbSjgP", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "YJbEv33TSHQq6wcmM", "msg": "There are 5 possible tokens that can appear here:\nenum fun let open pred", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-1-7 13:27:42"} {"_id": "KWdFpLWWGqZZys3uL", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n2 in n1.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "5sTxGdm2fNSgrX8Cp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 11:06:46"} {"_id": "RTZXMbuEpYjewZFzh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "NP82CKdPFhkvkCLy6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:54:18"} {"_id": "YxkBiTpp3JHKtnnx5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *(~adj).x \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "nB49BsZ95t7mMmfPm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 08:25:47"} {"_id": "v5LgvYm7XBDinQ4FF", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n ! undirected\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n: Node| n in n.adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "fmZqRrFB2QJfb7ubx", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-6 20:49:37"} {"_id": "YtLLCLkjwTQePSywp", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JvLwKxJkMfzoFq7CP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:19:47"} {"_id": "LaiFcyxc5wBJbFMNM", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2:Node | n1->n2 in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n1:Node | n1 not in adj.n1 \n\t \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1,n2:Node | n1 in adj.n2 and n2 in adj.n1\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "TkRgMdLuAzQBTbM5Q", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:57:04"} {"_id": "ju7tRYQ7jvzhTsixB", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n\n}\t\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AD5iJBxhraqmtKqPX", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-7 13:28:51"} {"_id": "2QX4hhxS7swZJrGph", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n \n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "HzgA5ju3QfGt6iXXX", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 444, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 10:41:33"} {"_id": "mwErw7ZWCMusvp6BG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(~adj +adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj+n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2nFicSBQcobiTsGy2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-7 12:29:22"} {"_id": "oik9A9zaeHAzv3pfG", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dDCJFWA36uQJbS2FA", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-2-3 00:16:28"} {"_id": "8AmBwStbPZ8zL4G5B", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj & n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Yxfimmjb4f8pwwi2G", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:48:15"} {"_id": "2LSYHQiLi3wRMbPPa", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n *adj + *(~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "Crt9T8e8cSWJXs8iz", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:24:11"} {"_id": "EMaYaBby2m6QJFJW8", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | Node = (n.^adj + n.^(~adj) + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | Node = (n.^adj + n)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) and (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "PGREf5b8jLn5wF5La", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:57:19"} {"_id": "qgwHf53xydHWncdH7", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oEqbfzmvcPZLQkQxb", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-9 23:02:37"} {"_id": "mqegQPxwX7PhfabNP", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in v.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall v1,v2,v3:Node | v1->v2 in adj and v2->v3 in adj implies v1->v3\n}", "derivationOf": "HeH7tY6PSgQfRgpm6", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:56:38"} {"_id": "SLXuxNSmnvWmExdF6", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qbrepD25Sb7i6BkdQ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-2 10:32:31"} {"_id": "DbAHdnWQdvtKwvvG7", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \nall n : Node | Node in n.^adj\n\n }\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "kg3CmxMSRBSCJq7Sd", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-2-3 07:38:48"} {"_id": "2FWzBhMA9XJFAaK3r", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x, y : Node | x->y in adj implies not y->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DHuhvp5s5CyhEx4F5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:39:37"} {"_id": "GkK4Nao4vXH862xJj", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + e1.~*adj + *adj.e1 + ~*adj.e1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall e1 : Node | Node in (e1.*adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TJyyHd3byy9GLTj8R", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:29:51"} {"_id": "dAXPJoBt76PXdjmji", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n some n:Node | Node in (n.^adj +n)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "aMaRMPmYjYjXW2Zsa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 11:59:20"} {"_id": "brLAADHfCxQTtuJ8N", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \n \n \n \n \n all a,b : Node | a->b in adj\n \n \n \n \n \n \n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "K5Q3463NSLrRz6MMP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 16:09:55"} {"_id": "eAgx8ySzyD4NYB8ZR", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "JbhZZ5xL2Sm3vaP3S", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-9 22:23:18"} {"_id": "keb3kgu6Sfn4kQY5r", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hjjgkPJQHht7nZpGb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:04:27"} {"_id": "nH4sCaCw85cieSfzj", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + ~*adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "u3jypFdNGKtKbDkFA", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:34:05"} {"_id": "Zpqzxa7sswfKQD2xd", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n = n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | n->(n.^adj) in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "qqQuxqdWg7CCvr4qe", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 02:36:27"} {"_id": "GbThHNvj787EPo2JT", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | no (n in n.^adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ni4YmaoJ7ebXuubkw", "msg": "This expression failed to be typechecked line 47, column 15, filename=/tmp/alloy_heredoc13685675447246597982.als", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-27 05:00:45"} {"_id": "spX7bkf2bQr8i8QdS", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall Node a,b | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tnot (Node.adj = )\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eAjRQJbeBLESGydth", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:12:16"} {"_id": "fRQrMeabNCYhRq9XK", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node - n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NytGbdE3bu2EzeL9r", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 17:58:30"} {"_id": "JxFth7dBQhinnr53C", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all n : Node | no (n.adj & n.(~adj))\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n : Node | no (n.^adj & n)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n:Node | Node in n.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj \n}", "derivationOf": "FCNiHrsTDKnckzvaY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:10"} {"_id": "wzNTa64HseYcZoFfS", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t~adj != adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FsdCeYSB6oWCNqhWJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-19 14:48:06"} {"_id": "SwdLhTyEaWH2tmPg6", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "h6C22aYtn9JbkXd6B", "msg": "The name \"node\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-12-1 19:04:56"} {"_id": "qyPwwCQniJrTDqCzA", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | adj.n in n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xhmvRFoNx42BSWav6", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:04:15"} {"_id": "BiefHMJdGbDGoA35h", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall b:Node | b in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "4D6f5mM2m82EDBHw7", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:04:34"} {"_id": "qrgvQp2h6kzDWQwgJ", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tall n : Node | n->n.adj.adj in adj\n\n}", "derivationOf": "cZ7oq9JJakFawfDnw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 23:11:06"} {"_id": "7gFr8dNmQtCP9NNKQ", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | n->(n.adj)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PrfDQzeEarwzbvMxb", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:44:47"} {"_id": "pDmm4d3nCk3Yug3Xv", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^adj = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "TKjnZpxzXQXdZKCN2", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:26:37"} {"_id": "c5jCqD5E4e3RP5APg", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj + adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PoFPFWjqyYFenkXgp", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:27:19"} {"_id": "TFH2x8oSYsWnhwFG3", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^adj = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "HNbGpGe96gymuz9dY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:22:26"} {"_id": "FGN837ePK2vfwPhSM", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno ~adj & adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n} \n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (adj & iden)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}\n\n\n\n", "derivationOf": "s4HncYwwCin8j7uGT", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 15:12:32"} {"_id": "G3s2yBNxWhoJTFnFC", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n: Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n: Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cYRCGLf9MYDjbrp7z", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:30:53"} {"_id": "wTnEQZpHwDtqXg9KJ", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LdSo3tCNb8geo6mwu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:45:00"} {"_id": "j8dXSKufYdNSSFNy8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj \n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "AnAm6jSq8KLPSrEyj", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-1-8 19:54:38"} {"_id": "hmbJwAto3LtSYod5d", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t(Node -> Node - iden) in ^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tno (adj . adj)\n}", "derivationOf": "JgRNLghuAA6s5M8hk", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:29:15"} {"_id": "uwqwR6EXx7s3jWZzS", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj and n->n in adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "yEHFemNMWzZm8NsHL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-10 22:30:22"} {"_id": "ui5CZSLTCEJxCsZb9", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "PtZt9567diAzXrCMK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:25:52"} {"_id": "9NfRcHT3Tx7gQqBFG", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n not in adj.n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t all x : Node | Node in x.*(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \tall n : Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qgwHf53xydHWncdH7", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-9 23:02:49"} {"_id": "7rZxXeQQYFwPr8uT4", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t all n, n1 : Node | n->n1 in adj => n1->n not in adj\n\t\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj & ~adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n, n1, n2 : Node | n->n1 in adj and n1->n2 in adj => n->n2 in adj\n}", "derivationOf": "N87TtbjmeogFcagiW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-10 18:54:07"} {"_id": "MB6CQ5HBfdMLPuTnT", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | adj(n1,n2) implies adj(n2,n1)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "G9igdN6T3yccnfHNE", "msg": "There are 1 possible tokens that can appear here:\n)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:00:44"} {"_id": "7PzFmHBYRa8eBE4PE", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "DztoFdw5sjsnMvrh5", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 17:43:22"} {"_id": "BfzxXSYXC7xs6mgQw", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "FbzJPd278u6HPBbps", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:27:13"} {"_id": "8AkSEkDhnb9v2RApy", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KMwvNi8Lom7daQA6Z", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:32"} {"_id": "qdn64ytJSHzD37uAo", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n(Node -> Node) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j3LQhme4cm8hGcaWF", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 22:20:12"} {"_id": "rCTnnMzuy9wXq3LZi", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj + n)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "YcRvQ872FDyqcZqDa", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-11 11:57:25"} {"_id": "aRR9xYXLap7dPzxh3", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\nall disj x,y : Node | x in y.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n\tall n : Node | Node-n in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2:Node | n2 in (n1.adj).adj implies n2 in n1.adj\n\n}", "derivationOf": "tRHcTP2tSt48J4PAF", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-27 05:41:06"} {"_id": "dWKqm4vFyqBWtWZ8E", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "cnByvE2K39CmYjDu9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:16:25"} {"_id": "AbErnEiw4edEmokSe", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj & ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SEsN5pmfitwXTACP6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-4 16:37:21"} {"_id": "8bvioCHwnTs8SEW3g", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n ^adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | n.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.*adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \n ^adj in adj\n}", "derivationOf": "jwJBkwLm44wzAjt7x", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:14"} {"_id": "6WzTkSNPuavYnpQwJ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sewBk2hL4L8rmEpd4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:36:09"} {"_id": "NrJdrZRe4QZb45QN6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xJZX8xEDEQ65s8Wu9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-19 14:47:43"} {"_id": "wSYT7CJ9tau9bWGii", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node -> Node\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "628xQYZyLc5yL34ti", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-12-3 09:38:30"} {"_id": "JLskqLPYLqHGw7RMP", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:07:55"} {"_id": "4iauYf8qgxfMSvfCs", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj and n.^~adj\n}\t\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TC4TEQrF4DhYb4Geo", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-10 15:55:00"} {"_id": "BLcfk8q7BhnACYqk3", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "72zmq89ZkSMcBX3cB", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:22:21"} {"_id": "Gy4tkXTzuphg3PapM", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj = adj.^adj\n}", "derivationOf": "HFwTDHu2YYvqnY9tg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:55:21"} {"_id": "7QXs37HTyF6si9djs", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node , a:Node | n->a in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "S6zmfRAAWNdDH9gK4", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:34:51"} {"_id": "xXQqP7CDJyJwvgpeh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^(adj + ~adj) = Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "jB24y2DoR8k9ZKqjE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:28:31"} {"_id": "ZFicZu2Y7M6DT8b6J", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3HogE8XHkhYMMuLzq", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:32:22"} {"_id": "XapQvYWg2W3ovXP4T", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n:Node | \n}", "derivationOf": "abrzRzAzyibodeq9S", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:32:45"} {"_id": "GnRMhShBAp6i3uyjG", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "H3R3MBtFFZibw7ucw", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:16"} {"_id": "oFPcMykNmbnxEGL8T", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-12 00:05:58"} {"_id": "y98CC8tGQBhHuGkL2", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x in ^adj.y and y in ^adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TmF7SnJ23EnCoyxb8", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:18:50"} {"_id": "AYbdXtQdaEsRRHnjX", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 && n2->n1 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "qFPFJFq82HSP59QGy", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:34:40"} {"_id": "xXvE5C4hw2rmxpJiM", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tadj = no Node -> ~Node\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bAvDq4vMTDdcwTgH2", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:41:11"} {"_id": "3HogE8XHkhYMMuLzq", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cwkauwB7FLv7y3XZS", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-16 18:29:06"} {"_id": "9sMuGuqDLcTQawBtT", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node,b:Node | a in a.^adj implies a->b in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pKCyjNiZBmbcCbrDE", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:38:34"} {"_id": "QnWmLv7tPtdHDM9eB", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bQ4ywFrDe7e5EzRWC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:02"} {"_id": "T32GzoLs6mhmXAh8F", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\nall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "enQaDcNyd5wSFEg9F", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:28:27"} {"_id": "ARDzqpQB2HfvrCaKs", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | some n1.adj:>n2 implies some n2.adj:>n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | some n1.adj:>n2 implies no n2.adj:>n1\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node | some n1.adj:>Node implies (n1 not in n1.^adj:>Node)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1:Node | n1.adj:>Node = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1,n2:Node | some n1.adj:>n2 implies n1 != n2\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1:Node | ((^adj.n1:>Node) + (n1.^adj:>Node)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n1:Node | n1.^adj:>Node = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | some (n1.adj:>n2) and some (n2.adj:>n3) implies some n1.adj:>n3\n}", "derivationOf": "GmXYbPzHaNXzxPYju", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:19:46"} {"_id": "hCWfePSvhB5B7F99N", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n}\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sXrAYh2PBL6NZXz52", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 20:38:50"} {"_id": "NkzAZAqjqQ4zH5677", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node.^adj \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "vZA56bT7MZKudfiKp", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:58:07"} {"_id": "dDCJFWA36uQJbS2FA", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall disj n : Node | n in adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "bXpxKhtqY224iNTHM", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-2-3 00:16:03"} {"_id": "DNbRpL526sZr6joBf", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t^(adj + ~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "dTatQNDGS2tba2WGA", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 11:02:02"} {"_id": "rgcxWyyWjr9Yhfatr", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "ETEFiWNggEJXvAAsh", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:29:54"} {"_id": "w6cRf6mkyJkHFaDjB", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | x & (^adj).y\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-16 19:11:20"} {"_id": "NQfzD8KnDFPSedErb", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NpEP8K7JS8cFPKZ5L", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:33:35"} {"_id": "ETEFiWNggEJXvAAsh", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xBqhJzurZF5HQasH9", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:29:25"} {"_id": "Gtadq9esuidC9BYda", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tn.adj.adj.Node\n\n}", "derivationOf": "Lai6LmFvk9vY8Hts8", "msg": "The name \"n\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 23:00:16"} {"_id": "z5nwADSAhiS4NQ7sE", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \t\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tall n, n1 : Node | n->n1 in adj and n1->n in adj => n1 = n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9RxubbggiBWMxe9EY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-6 01:42:17"} {"_id": "eTT5yPyat3qaFt5qL", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no x->x\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:18:48"} {"_id": "E97Fd7qibkcDPdyXa", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "tPMTAatjEyadf8Z72", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-7 16:43:49"} {"_id": "ZvhsnrRLmGNqRo98c", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n(Node -> Node - iden) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qdn64ytJSHzD37uAo", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:20:22"} {"_id": "YQ9YAJwzfwdxwLQC8", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n\t\n\tall n1:Node | Node in (n1.adj +adj.n1)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "3EBDauMJyEdjCStte", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-9 13:18:57"} {"_id": "iZKQQAS8TEEXJhh3z", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\t~iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2TkjxdEo6BKJgr3Wu", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{univ->univ}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:46:24"} {"_id": "QeJuw3TDAxFhQnvnY", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = adj + ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n all n: Node | n not in n.^adj\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n: Node | n.adj = Node - {n} \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "SQfDMkt2AkKMq5nNm", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-7 17:37:27"} {"_id": "n8dJhmQDNT7hgAtC3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall x,y:Node | x->y in adj implies y->x not in adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node-n in n.^adj \n \t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "g7fJtsdWm7FymsDmu", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-27 04:55:27"} {"_id": "3uNA8nafpStupQyy4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1 : Node | n1.adj = adj.n1\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n1:Node| some n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pLfRZSnHWjrvqhtLT", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:28:30"} {"_id": "iPqgmP7YZYBXQZnKG", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n : Node | Node in n.*adj + ^adj.n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5pFowB8Liqryj2Mme", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 07:50:09"} {"_id": "cikJhLAbNk3nZ6qiy", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall disj n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dFuNamzLzFA5ixJeC", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:23:25"} {"_id": "JsaW5q5Bmdmsqy9k3", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "Fy6bxEx4P6CXhHY24", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 02:47:56"} {"_id": "3AT3J4BH8BiwJgyza", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*adj).x\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "dgxo3wxvvXmezFX4X", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 21:17:24"} {"_id": "hhsfxaenckZEp7mS6", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n one Node or (Node = (Node.(^adj) + Node.(^(~adj))))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n one Node or (Node = Node.(^adj))\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "sa32uQE8AfCJDBX7W", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-16 03:43:29"} {"_id": "fEsvvKKF3iXPAAjns", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | (Node - n) in n.^adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CiHuLmdaWohoFKpwp", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 17:39:31"} {"_id": "c3bqRyz2ACP2BaBr7", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n \tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n *adj not in iden\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "mXvEaipP9ptRxF95R", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 09:50:33"} {"_id": "ezp2zb2gXEHT2RD7h", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "km3sW3DrTRxZoNveP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:30:42"} {"_id": "RMQe4QvP6GXXFjTwJ", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2: Node | n1->n2 in adj implies no n1->n2 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:54:06"} {"_id": "bFqtA7DL6J8vD2sGZ", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n: Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "uQtgCbphsFAHGn6Ld", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:13:24"} {"_id": "aXweizAbGX5cS8Mg3", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:17:06"} {"_id": "DJfn2bPHZ27XxPRkd", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "tuBxkQuHakxtCFkxX", "msg": "There are 1 possible tokens that can appear here:\n.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-16 03:47:13"} {"_id": "bkFZjQfLFwd2WhoG5", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj - ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aYdFyn9kLvgexZzMa", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:28:36"} {"_id": "B6pLpfe92MMiDCkuZ", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | b->a in adj implies a->b in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | no a.^adj & a.~(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "w8sAfonm8fa7eHTgP", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:27:05"} {"_id": "jKtw4yQThN57qtTyF", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-12 19:27:51"} {"_id": "iyeH4wFBisXJcP7dG", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n \tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node.^adj or Node.~^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "8b6jHFB92qD7PXg5u", "msg": "= can be used only between 2 expressions of the same arity, or between 2 integer expressions.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:56:38"} {"_id": "72zmq89ZkSMcBX3cB", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "aXweizAbGX5cS8Mg3", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:22:04"} {"_id": "vfnxZc3NdxGex724s", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj+n.^~adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "KW2jgNyaWn6CYAsgB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-12-1 19:01:08"} {"_id": "dNwMWGmgYDxL7yD5N", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall x, y : Node | some x<:(^adj.y) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "oiDoWRapoErxrbBkG", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:12:56"} {"_id": "yNkZCf5Gu2RsYAFbh", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n \tall n:Node | Node in n.^(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "Kov8hD65s7dsuLm8i", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:38:27"} {"_id": "jyf9jpXt3fEWRv3QD", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n\t some adj & Node in (Node.adj + adj.Node)\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n \n\t\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n}", "derivationOf": "4FgFJfkb3avKQr5TD", "msg": "& can be used only between 2 expressions of the same arity.\nLeft type = {this/Node->this/Node}\nRight type = {this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 13:12:05"} {"_id": "HNbGpGe96gymuz9dY", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n ^adj in Node->Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "oisjGf4FHY7ybsDNY", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:22:15"} {"_id": "5n6jaEbchxeGN2Yu4", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "uXwT7CQyaWYJhb9sM", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:44"} {"_id": "q2P9o3Tjjw4EnKxK9", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall adj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:16:51"} {"_id": "uJ8HLkcTPniJjSHWE", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall a:Node | a in adj.a\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9PJWKbiDGtS9faxXi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:35:20"} {"_id": "qqRNpidats9s8J74g", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (n.^(adj + ~adj)) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n : Node | n.^adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ComPvPPfGGhWHiw2d", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:23:27"} {"_id": "WFMWrqSsukK44MdzD", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "nd4b7pkrTNGZZJ64X", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:54:42"} {"_id": "EYjijPu3nGu3HjNwa", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | ((n1->n2 in adj) & (n2->n3 in adj)) implies (n1->n3 in adj)\n}", "derivationOf": "kw96r3TQJA6i2kBu7", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-16 03:39:12"} {"_id": "kGTGD6TZmrHsAGZd6", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | not n->n in adj\n all n: Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2, n3: Node | n1->n2 in adj and n2->n3 implies n1.*n3 in adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "FCTuGJwv8niMvk4n2", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 18:00:13"} {"_id": "qEjpYo4nagjLuJNXZ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NpxCfq3PeouMH7zxh", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:26:40"} {"_id": "y6KWYG37iJ4E2Dec2", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n all n : Node| all a : n.adj | n in a.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node| all a : n.adj | n not in a.adj\n\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "hqeFGniFikj8EMscG", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:26:54"} {"_id": "8CYPoPfwKjJgKFeBR", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/ \npred undirected {\n\tall n:Node | n.adj in adj.n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n:Node | not (n.adj in adj.n)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5KYTD6LvDL8HBqFnL", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:13:17"} {"_id": "GgqzDWP4dujBZf6C4", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n no adj.~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "ckfpPgKf38rx5BmDw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-11-10 16:08:03"} {"_id": "YFga9QdeMJAtyb6wP", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tadj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "LnGrGqnjjki4F2Ls9", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:28:13"} {"_id": "NXpoLgqq7iYbrep4X", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all n1,n2 : Node | n1.adj = n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-25 16:24:14"} {"_id": "6gu9tsuB5jRdKh3zt", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-14 09:14:10"} {"_id": "f8TzvFQMvFtWau69Y", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n \tall a:Node | a not in a.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "cXMpcWcKR3oBnq85b", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:49:17"} {"_id": "Fm7xWusqegp8HESC3", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "AeP4BqmC9ZyC35oaw", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-12-3 09:30:21"} {"_id": "kGMGzxS9AGg3pwvpn", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "qe2fBD59CHnE5CJkk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 09:16:29"} {"_id": "T3bn3xPeDbXAxpFop", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n Node | some n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wKoirFWZgo72X3TMn", "msg": "The \"all x\" construct is no longer supported. If you know the range of possible values of x, consider rewriting it as \"x == set_of_all_possible_values\".", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-11-11 11:52:11"} {"_id": "zqw65Qhn7e7D4kbgP", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | (Node-n) in n.adj \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QSMupbEutHnuaE9hg", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-15 17:06:56"} {"_id": "FfCAwNKTfMAnBAmf6", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + (*adj).x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj \nr\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n}", "derivationOf": "MMpgCXocthGHk2e6Y", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 09:48:59"} {"_id": "kD2QxxHqb9RjTn8cJ", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b: Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "HdDLRGizwXb74DYFE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-8 19:52:58"} {"_id": "DAhmNHdT4Ykjnd382", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj\n}\npred undirected1 {\n \tall n:Node | (n.adj in adj.n) \n\t\n}\n\npred undirected2 {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented1 {\n\tall n1,n2 :Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n\npred oriented2 {\n\t\n}\npred oriented3 {\n\tno (adj & ~adj)\n}\n\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \tall n :Node | n not in n.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1,n2 :Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n1:Node | n1->n1 not in adj\n}\n\npred noLoops1 {\n\tall n1:Node | n1 not in n1.adj \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode in Node.adj + adj.Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\u00b4\tNode in Node.adj & adj.Node \n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3 :Node | (n1->n2 in adj and n2->n3 in adj) implies n1->n3 in adj \n}", "derivationOf": "ARwjpde9BDQEmGQuJ", "msg": "Syntax error at the ? character. HEX: \\u3f)", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-9 11:18:08"} {"_id": "gSJ6PtQwxNcWKuDM3", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \nall n : Node | n in n.adj.~adj}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n \n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "D8qpy8dgeeXrXQtNX", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 10:43:25"} {"_id": "MiBJFQMcroETWrYfE", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "xLKjGE4D7ERNY6B5E", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:16:38"} {"_id": "JvMdXe89FhMtr8jra", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no iden & adj.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n no iden & ^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n adj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n no iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.*(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n *adj = Node->Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n adj.adj in adj\n}", "derivationOf": "hJL5aXZdZdxRApTNW", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-12 00:31:05"} {"_id": "J2BPNDhzxPvaPm7Ec", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a,b : Node | a -> b in adj implies b -> a in adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented { \n\t\n \tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall a : Node | a not in a.^adj \n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\tall a,b : Node | a -> b in adj \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GWRKcsM85jkgSse4a", "original": "gAeD3MTGCCv8YNTaK", "theme": {"currentFramePosition": {}, "currentlyProjectedSigs": [], "generalSettings": {"currentLayout": "breadthfirst", "metaPrimSigs": [{"parent": null, "type": "univ"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}, {"parent": "univ", "type": "Int"}, {"parent": "univ", "type": "Node"}, {"parent": "univ", "type": "String"}, {"parent": "null", "type": "univ"}, {"parent": "Int", "type": "seq/Int"}], "metaSubsetSigs": []}, "nodePositions": {"Node": {"x": 470.3937683105469, "y": 199}}, "relationSettings": {"edgeColors": [{"color": "#0074D9", "relation": "adj"}], "edgeStyles": [{"edgeStyle": "solid", "relation": "adj"}], "showAsArcs": [{"relation": "general", "showAsArcs": true}, {"relation": "adj", "showAsArcs": true}], "showAsAttributes": [{"relation": "adj", "showAsAttributes": false}]}, "sigSettings": {"nodeBorders": [{"border": "solid", "type": "univ"}, {"border": "inherit", "type": "Int"}, {"border": "inherit", "type": "Node"}, {"border": "inherit", "type": "seq/Int"}], "nodeColors": [{"color": "#2ECC40", "type": "univ"}, {"color": "inherit", "type": "Int"}, {"color": "inherit", "type": "Node"}, {"color": "inherit", "type": "seq/Int"}], "nodeShapes": [{"shape": "ellipse", "type": "univ"}, {"shape": "inherit", "type": "Int"}, {"shape": "inherit", "type": "Node"}, {"shape": "inherit", "type": "seq/Int"}], "nodeVisibility": [{"type": "univ", "visibility": false}, {"type": "Int", "visibility": true}, {"type": "seq/Int", "visibility": true}, {"type": "general", "visibility": false}, {"type": "Node", "visibility": false}]}}, "time": "2019-10-17 11:03:03"} {"_id": "AAwAxBrd6vn4NkaYX", "cmd_i": 1, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2: Node | n1.n2 in Node implies no n1.n2 in Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "RMQe4QvP6GXXFjTwJ", "msg": "This cannot be a legal relational join where\nleft hand side is n1 (type = {this/Node})\nright hand side is n2 (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:55:10"} {"_id": "joGs3DnJRbyuDYg9g", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2:Node | n1 in n2.adj implies n2 in n1.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2:Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n1, n2:Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n1, n2:Node | n2 in n1.*(adj+~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1, n2, n3:Node | n1->n2 in adj and n2->n3 in adj implies n1->n3 in adj\n}", "derivationOf": "LzKrLcHDE5JSh2AZk", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-1-21 18:40:34"} {"_id": "upnNKoEYLqvFSanqm", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t no adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tsome Node\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no (^adj).n & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | some n.(^adj)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\t\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "jPAoE7mhu9vy7NHet", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:26:01"} {"_id": "dowZHEnPPAahqaTTz", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "q2X9fXbkD63y2ifHn", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:40:08"} {"_id": "929LZEaH29LuwaywE", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall a:Node,b:Node | a->b in adj implies b->a in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\t\n \tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t all a:Node | a not in a.^adj \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \t\n\t\n \tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall a:Node | not a->a in adj\n \n}\t\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected { \n\tall a,b:Node | a.^adj = b\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall a,b,c:Node | a->b in adj and b->c in adj implies a->c in adj\n}", "derivationOf": "WsNeBoevgMHXyqP4v", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:59:56"} {"_id": "aT982RPaXRfKRz4Dr", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "CWhx6AedHW7zBpLFD", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 18:15:15"} {"_id": "PhMif6zdGpbnbZ6j7", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tno (iden & ^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tNode->Node in *(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tNode->Node in *adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n\n}", "derivationOf": "KYyW3odtGFuXJHhnC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-12 16:19:16"} {"_id": "w3QTiGJXCTM769eMe", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "BM88cwyneH25nvP2H", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-10 15:48:13"} {"_id": "3Rd8SwjDBtdFC2mtv", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | some (n1->n2)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | no (n->n)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all n1, n2, n3 : Node | (some (n1->n2) and some (n2->n3)) implies some (n1->n3)\n}", "derivationOf": "YZ7WD4sqAaMQThRLc", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:24:41"} {"_id": "eKcGuNeCfpzitPXai", "cmd_c": true, "cmd_i": 1, "cmd_n": "oriented", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n \t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | no n.^adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eAgx8ySzyD4NYB8ZR", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-12-9 22:23:23"} {"_id": "cjgB5DJEJhGuGc4cs", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n = n.^adj + n.^~adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "JAg7y2dd8qJtG9bEi", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:42:52"} {"_id": "sXrAYh2PBL6NZXz52", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n.adj = adj.n\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "f59AgZSYopLWRxGrH", "msg": "There are 38 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { } ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-13 20:38:31"} {"_id": "dFuNamzLzFA5ixJeC", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall disj n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tNode->Node in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "5sBPKmxcaAeiPcJuE", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-5 11:23:16"} {"_id": "45v3J3N8Q4SpbPhzA", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\t\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n \tall n1, n2 : Node | n1 in n2.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno iden & adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "DZDsf5tcKiuaw9PQi", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:49:04"} {"_id": "Q4nM45ZCH8qLFYjC6", "cmd_i": 5, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj=~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n : Node | (+adj.n + ^~adj.n) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "6TEm8m9GsoESzEteT", "msg": "There are 37 possible tokens that can appear here:\n! # ( * @ Int NAME NUMBER STRING String Time ^ after all always before disj eventually fun historically iden int let lone no none once one pred seq set some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:20:00"} {"_id": "DqqXAzgp2jssqPJbz", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj = ~adj\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x: Node | x not in x.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "yN7FK83qxRCJTk7am", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-8 15:11:47"} {"_id": "BYgRMEs2Qr45s38t2", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj & ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "9d4CR9rNLH4ihev7g", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2019-10-17 10:24:51"} {"_id": "mBu2oZwk4g98oTSi8", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all n1, n2 : Node | n2 in (n1.^adj + n1.^(~adj))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all n1, n2 : Node | n2 in (n1.^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "BSLJNCW8veoKKb84p", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 18:42:29"} {"_id": "6FfjnRxGtTTQFiqqJ", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-7-4 21:12:35"} {"_id": "HSiu2LXdf33K69sCd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in (n+ n.*adj + *adj.n).*adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "hRZLCLxa8SDNNAcyj", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 21:22:50"} {"_id": "5bKSKLQhcWJipx9qr", "cmd_c": true, "cmd_i": 7, "cmd_n": "transitive", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tno n:Node | n in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\t\n \tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops{\n\tno n:Node | n in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node in n.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\tall n1,n2,n3:Node | n1->n2 in adj and n2 -> n3 in adj implies n1->n3 in adj\n}", "derivationOf": "98A8tocBXmbKmtDjY", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-11-11 15:22:18"} {"_id": "b5x88vcyXebcBnyhM", "cmd_i": 6, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no adj - ~adj\n\t\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj & ~adj\n\t\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v : Node | no v.(^adj) & v\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall v : Node | not v->v in adj\n \t\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tadj = Node -> Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall v : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "GavfJWsg8Cp968xvD", "msg": "The name \"x\" cannot be found.", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:55:44"} {"_id": "ZG2wPbi8e8JEvyxRz", "cmd_i": 4, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = adj + ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2: Node | n1->n2 + n2->n1 in adj\n all n: Node | Node = n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n: Node | no n->n in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "TthbENRLPrbQRKyPi", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-7 17:52:31"} {"_id": "jDis82RxLXRohxqKw", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj.~adj in iden\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno ^adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "eyLDefH3KqqD5Yaz6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-14 09:16:57"} {"_id": "xhmvRFoNx42BSWav6", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | adj.n in n.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-17 10:03:56"} {"_id": "cTounfSycBe8kvTq7", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | no ~(n.adj)\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "gAeD3MTGCCv8YNTaK", "msg": "~ can be used only with a binary relation.\nInstead, its possible type(s) are:\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-18 02:17:09"} {"_id": "Dh3L5RdJhPo3nCwKC", "cmd_i": 2, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1, n2 : Node | n1->n2 in adj implies not n2->n1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\toriented\n \tall n : Node | n not in adj*\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "v7Tf2ffiGwTtbghPP", "msg": "There are 25 possible tokens that can appear here:\n( * @ Int NAME NUMBER STRING String Time ^ all fun iden let lone no none one seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:18:12"} {"_id": "PoFPFWjqyYFenkXgp", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\t\n \tno adj & adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies not v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall v1, v2 : Node | v1->v2 in adj and v2->v1 in adj implies not v1 = v2 & v1\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "iYnpMCyGqZzL7uxfB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:58"} {"_id": "idYRhcoxpck7snKRF", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj & ~adj = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no adj + ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nall n : Node | n.^adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n adj.~adj not in iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node.(adj + ~adj) = Node\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node.adj = Node\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "QnWmLv7tPtdHDM9eB", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 11:24:05"} {"_id": "u3jypFdNGKtKbDkFA", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\nhttp:\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n all x, y : Node | x->y in adj implies y->x in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n all x, y : Node | x->y in adj implies y->x not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all x : Node | no x.(^adj) & x \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all x : Node | x.adj = Node \n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all x : Node | not x->x in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n all x : Node | Node in x.*adj + *~adj.x\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n all x : Node | Node in x.*adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n all x, y, z : Node | x->y in adj and y->z in adj implies x->z in adj\n\n}", "derivationOf": "YuB7EKWxC8qiECrE5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-16 19:33:55"} {"_id": "wbt6Xnke2cWre4b8i", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | no n.(*adj) & n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "grbFe4YDzaekwkHxW", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-10-18 22:04:23"} {"_id": "vg8tFJW7vqQzdYEWy", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tall n1,n2 :Node | n1->n2 in adj implies n2->n1 in adj \n\tall n:Node | (n.adj in adj.n)\n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "p4RLEqCewGs2xMiCw", "msg": "There are 29 possible tokens that can appear here:\n# ( * @ Int NAME NUMBER STRING String Time ^ all disj fun iden int let lone no none one pred seq some sum this univ { ~", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 10:33:25"} {"_id": "5HdZtDhwh7TSPsQSR", "cmd_i": 7, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n adj in ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tadj & ~adj in iden\n}\n\n\n\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node->Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno (iden & adj)\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n : Node | Node in n.^adj\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n \tall n : Node | n.adj.adj.Node\n\n}", "derivationOf": "Gtadq9esuidC9BYda", "msg": "This cannot be a legal relational join where\nleft hand side is n . (this/Node <: adj) . (this/Node <: adj) (type = {this/Node})\nright hand side is this/Node (type = {this/Node})", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-10 23:00:27"} {"_id": "kCYgMbuarW7cc7b2W", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \n all n : Node | n.adj = adj.n\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n \n all n : Node | n not in n.adj.adj\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n \n \n all n : Node | n not in n.^adj\n \n \n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n \n all n : Node | (n + n.adj) in Node \n \n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n \n all n : Node | n not in adj.n\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \n all n : Node | n \n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "r9d7wkqGkds9Wwtje", "msg": "This must be a formula expression.\nInstead, it has the following possible type(s):\n{this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-15 16:28:48"} {"_id": "ZypM2XgpdZzHqtqgr", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n:Node | n in Node.adj or n in adj.Node\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "riXQABo88KZvRbg6R", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2021-1-13 20:37:42"} {"_id": "JDxTAWvLoA4TqHfWa", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | Node in (e1.*adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "sqAycZpLvaWhuHMx5", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:24:24"} {"_id": "mMGtE38MFg63Szu5W", "cmd_c": true, "cmd_i": 2, "cmd_n": "acyclic", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "j2rrRCQSYT5tMW5tH", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2019-12-2 10:49:53"} {"_id": "j3LQhme4cm8hGcaWF", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\nall n1, n2 : Node | n1->n2 in adj implies n2->n1 not in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\nall n : Node | n not in n.(^adj)\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\nadj = (Node -> Node)\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\nno adj & iden\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n(Node -> Node) in ^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "2eGnbYnw3Da3B2Nzf", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2021-1-13 22:20:09"} {"_id": "q9QSfwuqcjHDSqLEQ", "cmd_i": 3, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2 : Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2 : Node | n1 in n2.adj implies n2 not in n1.adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.adj.*adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "csN57YKYRKy9kfs7o", "msg": "in can be used only between 2 expressions of the same arity.\nLeft type = {this/Node}\nRight type = {this/Node->this/Node}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2021-1-9 22:47:42"} {"_id": "H2G4wuwCX8nG9eRaE", "cmd_c": true, "cmd_i": 0, "cmd_n": "undirected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n : Node | some adj.n \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "3R4FWoEx2AfM8j8Kt", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:28:52"} {"_id": "ywkC4zH8GF4NQZuMz", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n \tadj in ~adj \n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall e1, e2 : Node | e1 -> e2 in adj implies e2 -> e1 not in adj\n \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall e1 : Node | e1 not in e1.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tadj = Node -> Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall e1 : Node | e1 not in e1.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall e1 : Node | (Node - e1) in (e1.*adj + *adj.e1) \n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "TENr5jM2GSSX49ExJ", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-5 09:26:39"} {"_id": "mnTxyTRX4aKnRZjJM", "cmd_c": true, "cmd_i": 3, "cmd_n": "complete", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n (adj & ~adj) = adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n all n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n all n1, n2 : Node | n1->n2 in adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n : Node | n->n not in adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n Node in (Node.(^adj) + Node.(^(~adj)))\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n Node in Node.(^adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \n}", "derivationOf": "xmJyGwpF9kyo4byDC", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-16 03:41:46"} {"_id": "yYPjy2jBkDdnoqpjT", "cmd_c": true, "cmd_i": 4, "cmd_n": "noLoops", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n no (adj - ~adj )\n\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n no (adj & ~adj)\n\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n : Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n : Node | n.adj = Node\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n all n:Node | n not in n.adj\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "wyyseoSPtcr384tnb", "original": "gAeD3MTGCCv8YNTaK", "sat": 0, "time": "2020-11-18 18:36:07"} {"_id": "bx5ucHXWpaY63PGrE", "cmd_i": 0, "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall v1, v2 : Node | v1->v2 in adj implies v2->v1 in adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall v1, v2 : Node | v1->v2 in adj implies no v2->v1 in adj\n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "NkRS7GxjhTxvr3inA", "msg": "This must be a set or relation.\nInstead, it has the following possible type(s):\n{PrimitiveBoolean}", "original": "gAeD3MTGCCv8YNTaK", "sat": -1, "time": "2020-11-5 09:13:42"} {"_id": "zkoSjFR4fiSksxrL5", "cmd_c": true, "cmd_i": 5, "cmd_n": "weaklyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tall n1,n2:Node | n2 in n1.adj implies n1 in n2.adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tall n1,n2:Node | n2 in n1.adj implies n1 not in n2.adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tall n:Node | n not in n.adj\n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n\tall n:Node | Node in n.^adj\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n\n}", "derivationOf": "pTqgtQJ8ui9Tewu9B", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2020-11-18 02:53:08"} {"_id": "2Kfs5Jr9fAhSFedEd", "cmd_c": true, "cmd_i": 6, "cmd_n": "stonglyConnected", "code": "/* \nEach node as a set of outgoing edges, representing a directed graph without multiple edged.\n*/\nsig Node {\n\tadj : set Node\n}\n\n/*\nThe graph is undirected, ie, edges are symmetric.\nhttp://mathworld.wolfram.com/UndirectedGraph.html\n*/\npred undirected {\n\tadj = ~adj\n}\n\n/*\nThe graph is oriented, ie, contains no symmetric edges.\nhttp://mathworld.wolfram.com/OrientedGraph.html\n*/\npred oriented {\n\tno adj & ~adj \n}\n\n/*\nThe graph is acyclic, ie, contains no directed cycles.\nhttp://mathworld.wolfram.com/AcyclicDigraph.html\n*/\npred acyclic {\n\tall n:Node | n not in n.^adj\n}\n\n/*\nThe graph is complete, ie, every node is connected to every other node.\nhttp://mathworld.wolfram.com/CompleteDigraph.html\n*/\npred complete {\n\tall n:Node | Node in n.adj\n}\n\n/*\nThe graph contains no loops, ie, nodes have no transitions to themselves.\nhttp://mathworld.wolfram.com/GraphLoop.html\n*/\npred noLoops {\n\tno adj & iden \n}\n\n/*\nThe graph is weakly connected, ie, it is possible to reach every node from every node ignoring edge direction.\nhttp://mathworld.wolfram.com/WeaklyConnectedDigraph.html\n*/\npred weaklyConnected {\n \tall n:Node | Node-n in n.^(adj + ~adj)\n}\n\n/*\nThe graph is strongly connected, ie, it is possible to reach every node from every node considering edge direction.\nhttp://mathworld.wolfram.com/StronglyConnectedDigraph.html\n*/\npred stonglyConnected {\n\tall n:Node | Node-n in (n.^adj + n.^~adj)\n}\n\n/*\nThe graph is transitive, ie, if two nodes are connected through a third node, they also are connected directly.\nhttp://mathworld.wolfram.com/TransitiveDigraph.html\n*/\npred transitive {\n \tadj.adj in adj\n}", "derivationOf": "ZEXea3QQj8vPPf7k6", "original": "gAeD3MTGCCv8YNTaK", "sat": 1, "time": "2019-10-17 10:40:03"}