0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n059.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 15:00:56 CST 2018
125.30/125.52	% done 20977 iterations in 125.310s
125.30/125.52	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
125.30/125.52	% SZS output start Refutation
125.30/125.52	tff(conj_5, axiom,
125.30/125.52	  (ord_less_eq(fun(nat,bool),kk,
125.30/125.52	               uminus_uminus(fun(nat,bool),
125.30/125.52	                             image(agent,nat,shrK,top_top(fun(agent,bool))))))).
125.30/125.52	tff('0', plain,
125.30/125.52	    ord_less_eq(fun(nat, bool), kk, 
125.30/125.52	      uminus_uminus(fun(nat, bool), 
125.30/125.52	        image(agent, nat, shrK, top_top(fun(agent, bool))))),
125.30/125.52	    inference('cnf', [status(esa)], [conj_5])).
125.30/125.52	tff(fact_98_sup__absorb1, axiom,
125.30/125.52	  (![A:$tType]:
125.30/125.52	     (semilattice_sup(A) =>
125.30/125.52	      (![X:A,Y:A]: (ord_less_eq(A,Y,X) => (sup_sup(A,X,Y) = X)))))).
125.30/125.52	tff('1', plain,
125.30/125.52	    ![X329 : $tType, X330 : X329, X331 : X329]:
125.30/125.52	      (~ ord_less_eq(X329, X330, X331)
125.30/125.52	       | sup_sup(X329, X331, X330) = X331
125.30/125.52	       | ~ semilattice_sup(X329)),
125.30/125.52	    inference('cnf', [status(esa)], [fact_98_sup__absorb1])).
125.30/125.52	tff('2', plain,
125.30/125.52	    (~ $true
125.30/125.52	     | ~ semilattice_sup(fun(nat, bool))
125.30/125.52	     | sup_sup(fun(nat, bool), 
125.30/125.52	         uminus_uminus(fun(nat, bool), 
125.30/125.52	           image(agent, nat, shrK, top_top(fun(agent, bool)))), kk)
125.30/125.52	        = uminus_uminus(fun(nat, bool), 
125.30/125.52	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
125.30/125.52	    inference('sup-', [status(thm)], ['0', '1'])).
125.30/125.52	tff(arity_HOL_Obool___Lattices_Olattice, axiom, (lattice(bool))).
125.30/125.52	tff('3', plain, lattice(bool),
125.30/125.52	    inference('cnf', [status(esa)], [arity_HOL_Obool___Lattices_Olattice])).
125.30/125.52	tff(arity_fun___Lattices_Osemilattice__sup, axiom,
125.30/125.52	  (![T_1:$tType,T_2:$tType]: (lattice(T_2) => semilattice_sup(fun(T_1,T_2))))).
125.30/125.52	tff('4', plain,
125.30/125.52	    ![X339 : $tType, X340 : $tType]:
125.30/125.52	      (semilattice_sup(fun(X339, X340)) | ~ lattice(X340)),
125.30/125.52	    inference('cnf', [status(esa)], [arity_fun___Lattices_Osemilattice__sup])).
125.30/125.52	tff('5', plain, ![X0 : $tType]: (~ $true | semilattice_sup(fun(X0, bool))),
125.30/125.52	    inference('sup-', [status(thm)], ['3', '4'])).
125.30/125.52	tff('6', plain, ![X0 : $tType]: semilattice_sup(fun(X0, bool)),
125.30/125.52	    inference('simplify', [status(thm)], ['5'])).
125.30/125.52	tff(fact_81_Un__commute, axiom,
125.30/125.52	  (![A:$tType,B2:fun(A,bool),A2:fun(A,bool)]:
125.30/125.52	     (sup_sup(fun(A,bool),A2,B2) = sup_sup(fun(A,bool),B2,A2)))).
125.30/125.52	tff('7', plain,
125.30/125.52	    ![X277 : $tType, X278 : fun(X277, bool), X279 : fun(X277, bool)]:
125.30/125.52	      sup_sup(fun(X277, bool), X279, X278)
125.30/125.52	       = sup_sup(fun(X277, bool), X278, X279),
125.30/125.52	    inference('cnf', [status(esa)], [fact_81_Un__commute])).
125.30/125.52	tff('8', plain,
125.30/125.52	    (~ $true
125.30/125.52	     | ~ $true
125.30/125.52	     | sup_sup(fun(nat, bool), kk, 
125.30/125.52	         uminus_uminus(fun(nat, bool), 
125.30/125.52	           image(agent, nat, shrK, top_top(fun(agent, bool)))))
125.30/125.52	        = uminus_uminus(fun(nat, bool), 
125.30/125.52	            image(agent, nat, shrK, top_top(fun(agent, bool))))),
125.30/125.52	    inference('demod', [status(thm)], ['2', '6', '7'])).
125.30/125.52	tff('9', plain,
125.30/125.52	    sup_sup(fun(nat, bool), kk, 
125.30/125.52	      uminus_uminus(fun(nat, bool), 
125.30/125.52	        image(agent, nat, shrK, top_top(fun(agent, bool)))))
125.30/125.52	     = uminus_uminus(fun(nat, bool), 
125.30/125.52	         image(agent, nat, shrK, top_top(fun(agent, bool)))),
125.30/125.52	    inference('simplify', [status(thm)], ['8'])).
125.30/125.52	tff(conj_6, conjecture,
125.30/125.52	  ((pp(aa(fun(msg,bool),bool,
125.30/125.52	          aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	          analz(knows(spy,evs2)))) | 
125.30/125.52	    pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
125.30/125.52	    ((~
125.30/125.52	       pp(aa(fun(msg,bool),bool,
125.30/125.52	             aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	             analz(knows(spy,evs2))))) & 
125.30/125.52	     (~
125.30/125.52	       pp(aa(fun(nat,bool),bool,
125.30/125.52	             aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	     (k != kab)) | 
125.30/125.52	    (~
125.30/125.52	      pp(aa(fun(nat,bool),bool,
125.30/125.52	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
125.30/125.52	            kk))) | 
125.30/125.52	    pp(aa(fun(msg,bool),bool,
125.30/125.52	          aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
125.30/125.52	          analz(knows(spy,evs2)))) | 
125.30/125.52	    pp(aa(fun(msg,bool),bool,
125.30/125.52	          aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	             aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	          analz(knows(spy,evs2)))) | 
125.30/125.52	    (aa(agent,nat,shrK,b) = kab)) & 
125.30/125.52	   (((pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
125.30/125.52	            kk)) | 
125.30/125.52	      ((~
125.30/125.52	         pp(aa(fun(msg,bool),bool,
125.30/125.52	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	               analz(knows(spy,evs2))))) & 
125.30/125.52	       (~
125.30/125.52	         pp(aa(fun(nat,bool),bool,
125.30/125.52	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	       (k != kab)) | 
125.30/125.52	      (~
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
125.30/125.52	              kk))) | 
125.30/125.52	      pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      pp(aa(fun(nat,bool),bool,
125.30/125.52	            aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
125.30/125.52	            kk)) | 
125.30/125.52	      (aa(agent,nat,shrK,b) = kab)) & 
125.30/125.52	     (pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
125.30/125.52	            kk)) | 
125.30/125.52	      ((~
125.30/125.52	         pp(aa(fun(msg,bool),bool,
125.30/125.52	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	               analz(knows(spy,evs2))))) & 
125.30/125.52	       (~
125.30/125.52	         pp(aa(fun(nat,bool),bool,
125.30/125.52	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	       (k != kab)) | 
125.30/125.52	      (~
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
125.30/125.52	              kk))) | 
125.30/125.52	      ((~
125.30/125.52	         pp(aa(fun(msg,bool),bool,
125.30/125.52	               aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	               analz(knows(spy,evs2))))) & 
125.30/125.52	       (~
125.30/125.52	         pp(aa(fun(nat,bool),bool,
125.30/125.52	               aa(nat,fun(fun(nat,bool),bool),member(nat),
125.30/125.52	                  aa(agent,nat,shrK,b)),
125.30/125.52	               kk))) & 
125.30/125.52	       (aa(agent,nat,shrK,b) != kab)))) | 
125.30/125.52	    pp(aa(fun(msg,bool),bool,
125.30/125.52	          aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	             aa(nat,msg,key,aa(agent,nat,shrK,a))),
125.30/125.52	          analz(knows(spy,evs2)))) | 
125.30/125.52	    ((~
125.30/125.52	       pp(aa(fun(msg,bool),bool,
125.30/125.52	             aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	                aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	             analz(knows(spy,evs2))))) & 
125.30/125.52	     (aa(agent,nat,shrK,b) != kab))))).
125.30/125.52	tff(zf_stmt_0, negated_conjecture,
125.30/125.52	  (~
125.30/125.52	    ((pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),k),
125.30/125.52	            kk)) | 
125.30/125.52	      ((~
125.30/125.52	         pp(aa(fun(msg,bool),bool,
125.30/125.52	               aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	               analz(knows(spy,evs2))))) & 
125.30/125.52	       (~
125.30/125.52	         pp(aa(fun(nat,bool),bool,
125.30/125.52	               aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	       (k != kab)) | 
125.30/125.52	      (~
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,a)),
125.30/125.52	              kk))) | 
125.30/125.52	      pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	               aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      (aa(agent,nat,shrK,b) = kab)) & 
125.30/125.52	     (((pp(aa(fun(msg,bool),bool,
125.30/125.52	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	              analz(knows(spy,evs2)))) | 
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
125.30/125.52	        ((~
125.30/125.52	           pp(aa(fun(msg,bool),bool,
125.30/125.52	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	                 analz(knows(spy,evs2))))) & 
125.30/125.52	         (~
125.30/125.52	           pp(aa(fun(nat,bool),bool,
125.30/125.52	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	         (k != kab)) | 
125.30/125.52	        (~
125.30/125.52	          pp(aa(fun(nat,bool),bool,
125.30/125.52	                aa(nat,fun(fun(nat,bool),bool),member(nat),
125.30/125.52	                   aa(agent,nat,shrK,a)),
125.30/125.52	                kk))) | 
125.30/125.52	        pp(aa(fun(msg,bool),bool,
125.30/125.52	              aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	                 aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	              analz(knows(spy,evs2)))) | 
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),aa(agent,nat,shrK,b)),
125.30/125.52	              kk)) | 
125.30/125.52	        (aa(agent,nat,shrK,b) = kab)) & 
125.30/125.52	       (pp(aa(fun(msg,bool),bool,
125.30/125.52	              aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	              analz(knows(spy,evs2)))) | 
125.30/125.52	        pp(aa(fun(nat,bool),bool,
125.30/125.52	              aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk)) | 
125.30/125.52	        ((~
125.30/125.52	           pp(aa(fun(msg,bool),bool,
125.30/125.52	                 aa(msg,fun(fun(msg,bool),bool),member(msg),aa(nat,msg,key,k)),
125.30/125.52	                 analz(knows(spy,evs2))))) & 
125.30/125.52	         (~
125.30/125.52	           pp(aa(fun(nat,bool),bool,
125.30/125.52	                 aa(nat,fun(fun(nat,bool),bool),member(nat),k),kk))) & 
125.30/125.52	         (k != kab)) | 
125.30/125.52	        (~
125.30/125.52	          pp(aa(fun(nat,bool),bool,
125.30/125.52	                aa(nat,fun(fun(nat,bool),bool),member(nat),
125.30/125.52	                   aa(agent,nat,shrK,a)),
125.30/125.52	                kk))) | 
125.30/125.52	        ((~
125.30/125.52	           pp(aa(fun(msg,bool),bool,
125.30/125.52	                 aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	                    aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	                 analz(knows(spy,evs2))))) & 
125.30/125.52	         (~
125.30/125.52	           pp(aa(fun(nat,bool),bool,
125.30/125.52	                 aa(nat,fun(fun(nat,bool),bool),member(nat),
125.30/125.52	                    aa(agent,nat,shrK,b)),
125.30/125.52	                 kk))) & 
125.30/125.52	         (aa(agent,nat,shrK,b) != kab)))) | 
125.30/125.52	      pp(aa(fun(msg,bool),bool,
125.30/125.52	            aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	               aa(nat,msg,key,aa(agent,nat,shrK,a))),
125.30/125.52	            analz(knows(spy,evs2)))) | 
125.30/125.52	      ((~
125.30/125.52	         pp(aa(fun(msg,bool),bool,
125.30/125.52	               aa(msg,fun(fun(msg,bool),bool),member(msg),
125.30/125.52	                  aa(nat,msg,key,aa(agent,nat,shrK,b))),
125.30/125.52	               analz(knows(spy,evs2))))) & 
125.30/125.52	       (aa(agent,nat,shrK,b) != kab)))))).
125.30/125.52	tff('10', plain,
125.30/125.52	    (pp(
125.30/125.52	       aa(fun(nat, bool), bool, 
125.30/125.52	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	           aa(agent, nat, shrK, a)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, a)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('11', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, a)), kk))),
125.30/125.52	    inference('simplify', [status(thm)], ['10'])).
125.30/125.52	tff('12', plain,
125.30/125.52	    (k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('13', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('simplify', [status(thm)], ['12'])).
125.30/125.52	tff('14', plain,
125.30/125.52	    (k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | aa(agent, nat, shrK, b) != kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('15', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) != kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('simplify', [status(thm)], ['14'])).
125.30/125.52	tff('16', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('17', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('simplify', [status(thm)], ['16'])).
125.30/125.52	tff('18', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | aa(agent, nat, shrK, b) != kab
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('19', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) != kab
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('simplify', [status(thm)], ['18'])).
125.30/125.52	tff('20', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))),
125.30/125.52	    inference('clc', [status(thm)], ['17', '19'])).
125.30/125.52	tff('21', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	             analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('22', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('simplify', [status(thm)], ['21'])).
125.30/125.52	tff('23', plain,
125.30/125.52	    (pp(
125.30/125.52	       aa(fun(nat, bool), bool, 
125.30/125.52	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	           aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('clc', [status(thm)], ['20', '22'])).
125.30/125.52	tff('24', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	               aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('25', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, k)), analz(knows(spy, evs2))))),
125.30/125.52	    inference('simplify', [status(thm)], ['24'])).
125.30/125.52	tff('26', plain,
125.30/125.52	    ~ pp(
125.30/125.52	        aa(fun(msg, bool), bool, 
125.30/125.52	          aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	            aa(nat, msg, key, k)), analz(knows(spy, evs2)))),
125.30/125.52	    inference('clc', [status(thm)], ['23', '25'])).
125.30/125.52	tff('27', plain,
125.30/125.52	    (k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) != kab),
125.30/125.52	    inference('clc', [status(thm)], ['15', '26'])).
125.30/125.52	tff('28', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('29', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('simplify', [status(thm)], ['28'])).
125.30/125.52	tff('30', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | aa(agent, nat, shrK, b) != kab
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('31', plain,
125.30/125.52	    (aa(agent, nat, shrK, b) != kab
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('simplify', [status(thm)], ['30'])).
125.30/125.52	tff('32', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))),
125.30/125.52	    inference('clc', [status(thm)], ['29', '31'])).
125.30/125.52	tff('33', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(msg, bool), bool, 
125.30/125.52	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	             analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('34', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('simplify', [status(thm)], ['33'])).
125.30/125.52	tff('35', plain,
125.30/125.52	    (pp(
125.30/125.52	       aa(fun(nat, bool), bool, 
125.30/125.52	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	           aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('clc', [status(thm)], ['32', '34'])).
125.30/125.52	tff('36', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	               aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('37', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))),
125.30/125.52	    inference('simplify', [status(thm)], ['36'])).
125.30/125.52	tff('38', plain,
125.30/125.52	    ~ pp(
125.30/125.52	        aa(fun(nat, bool), bool, 
125.30/125.52	          aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk)),
125.30/125.52	    inference('clc', [status(thm)], ['35', '37'])).
125.30/125.52	tff('39', plain, (aa(agent, nat, shrK, b) != kab | k = kab),
125.30/125.52	    inference('clc', [status(thm)], ['27', '38'])).
125.30/125.52	tff('40', plain,
125.30/125.52	    (k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))),
125.30/125.52	    inference('clc', [status(thm)], ['13', '39'])).
125.30/125.52	tff('41', plain,
125.30/125.52	    (pp(
125.30/125.52	       aa(fun(nat, bool), bool, 
125.30/125.52	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	           aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.52	           analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('clc', [status(thm)], ['40', '38'])).
125.30/125.52	tff('42', plain,
125.30/125.52	    (k = kab
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | ~ pp(
125.30/125.52	           aa(fun(nat, bool), bool, 
125.30/125.52	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	               aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.52	tff('43', plain,
125.30/125.52	    (~ pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.52	             aa(agent, nat, shrK, b)), kk))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(msg, bool), bool, 
125.30/125.52	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.52	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.52	     | pp(
125.30/125.52	         aa(fun(nat, bool), bool, 
125.30/125.52	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.52	     | k = kab),
125.30/125.52	    inference('simplify', [status(thm)], ['42'])).
125.30/125.53	tff('44', plain,
125.30/125.53	    (k = kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(fun(nat, bool), bool, 
125.30/125.53	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	               aa(agent, nat, shrK, b)), kk))),
125.30/125.53	    inference('clc', [status(thm)], ['43', '26'])).
125.30/125.53	tff('45', plain,
125.30/125.53	    (~ pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, b)), kk))
125.30/125.53	     | k = kab),
125.30/125.53	    inference('clc', [status(thm)], ['44', '38'])).
125.30/125.53	tff('46', plain,
125.30/125.53	    (k = kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))),
125.30/125.53	    inference('clc', [status(thm)], ['41', '45'])).
125.30/125.53	tff('47', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(msg, bool), bool, 
125.30/125.53	         aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	           aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	         analz(knows(spy, evs2))))
125.30/125.53	     | k = kab),
125.30/125.53	    inference('clc', [status(thm)], ['46', '26'])).
125.30/125.53	tff('48', plain,
125.30/125.53	    (k = kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(fun(msg, bool), bool, 
125.30/125.53	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	             analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.53	     | k = kab),
125.30/125.53	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.53	tff('49', plain,
125.30/125.53	    (~ pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, k)), analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.53	     | k = kab),
125.30/125.53	    inference('simplify', [status(thm)], ['48'])).
125.30/125.53	tff('50', plain,
125.30/125.53	    (k = kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), k), kk))
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(fun(msg, bool), bool, 
125.30/125.53	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	             analz(knows(spy, evs2))))),
125.30/125.53	    inference('clc', [status(thm)], ['49', '26'])).
125.30/125.53	tff('51', plain,
125.30/125.53	    (~ pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))
125.30/125.53	     | k = kab),
125.30/125.53	    inference('clc', [status(thm)], ['50', '38'])).
125.30/125.53	tff('52', plain, k = kab, inference('clc', [status(thm)], ['47', '51'])).
125.30/125.53	tff('53', plain,
125.30/125.53	    (aa(agent, nat, shrK, b) = k
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, b)), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('demod', [status(thm)], ['11', '52'])).
125.30/125.53	tff('54', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(nat, bool), bool, 
125.30/125.53	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	           aa(agent, nat, shrK, a)), kk))
125.30/125.53	     | aa(agent, nat, shrK, b) != kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.53	tff('55', plain,
125.30/125.53	    (aa(agent, nat, shrK, b) != kab
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('simplify', [status(thm)], ['54'])).
125.30/125.53	tff('56', plain,
125.30/125.53	    (aa(agent, nat, shrK, b) != k
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('demod', [status(thm)], ['55', '52'])).
125.30/125.53	tff('57', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(nat, bool), bool, 
125.30/125.53	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	           aa(agent, nat, shrK, a)), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, b)), kk))),
125.30/125.53	    inference('clc', [status(thm)], ['53', '56'])).
125.30/125.53	tff('58', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(nat, bool), bool, 
125.30/125.53	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	           aa(agent, nat, shrK, a)), kk))
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(fun(msg, bool), bool, 
125.30/125.53	             aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	               aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	             analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.53	tff('59', plain,
125.30/125.53	    (~ pp(
125.30/125.53	         aa(fun(msg, bool), bool, 
125.30/125.53	           aa(msg, fun(fun(msg, bool), bool), member(msg), 
125.30/125.53	             aa(nat, msg, key, aa(agent, nat, shrK, b))), 
125.30/125.53	           analz(knows(spy, evs2))))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('simplify', [status(thm)], ['58'])).
125.30/125.53	tff('60', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(nat, bool), bool, 
125.30/125.53	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	           aa(agent, nat, shrK, b)), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('clc', [status(thm)], ['57', '59'])).
125.30/125.53	tff('61', plain,
125.30/125.53	    (pp(
125.30/125.53	       aa(fun(nat, bool), bool, 
125.30/125.53	         aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	           aa(agent, nat, shrK, a)), kk))
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(fun(nat, bool), bool, 
125.30/125.53	             aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	               aa(agent, nat, shrK, b)), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('cnf', [status(esa)], [zf_stmt_0])).
125.30/125.53	tff('62', plain,
125.30/125.53	    (~ pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, b)), kk))
125.30/125.53	     | pp(
125.30/125.53	         aa(fun(nat, bool), bool, 
125.30/125.53	           aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	             aa(agent, nat, shrK, a)), kk))),
125.30/125.53	    inference('simplify', [status(thm)], ['61'])).
125.30/125.53	tff('63', plain,
125.30/125.53	    pp(
125.30/125.53	      aa(fun(nat, bool), bool, 
125.30/125.53	        aa(nat, fun(fun(nat, bool), bool), member(nat), 
125.30/125.53	          aa(agent, nat, shrK, a)), kk)),
125.30/125.53	    inference('clc', [status(thm)], ['60', '62'])).
125.30/125.53	tff(fact_19_UnCI, axiom,
125.30/125.53	  (![A:$tType,A2:fun(A,bool),B2:fun(A,bool),C2:A]:
125.30/125.53	     (((~pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),B2))) =>
125.30/125.53	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),A2))) =>
125.30/125.53	      pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C2),
125.30/125.53	            sup_sup(fun(A,bool),A2,B2)))))).
125.30/125.53	tff('64', plain,
125.30/125.53	    ![X54 : $tType, X55 : X54, X56 : fun(X54, bool), X57 : fun(X54, bool)]:
125.30/125.53	      (pp(
125.30/125.53	         aa(fun(X54, bool), bool, 
125.30/125.53	           aa(X54, fun(fun(X54, bool), bool), member(X54), X55), 
125.30/125.53	           sup_sup(fun(X54, bool), X56, X57)))
125.30/125.53	       | ~ pp(
125.30/125.53	             aa(fun(X54, bool), bool, 
125.30/125.53	               aa(X54, fun(fun(X54, bool), bool), member(X54), X55), X56))),
125.30/125.53	    inference('cnf', [status(esa)], [fact_19_UnCI])).
125.30/125.53	tff(fact_76_mem__def, axiom,
125.30/125.53	  (![A:$tType,A2:fun(A,bool),X2:A]:
125.30/125.53	     (pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2)) <=>
125.30/125.53	      pp(aa(A,bool,A2,X2))))).
125.30/125.53	tff('65', plain,
125.30/125.53	    ![X260 : $tType, X261 : fun(X260, bool), X262 : X260]:
125.30/125.53	      (pp(aa(X260, bool, X261, X262))
125.30/125.53	       | ~ pp(
125.30/125.53	             aa(fun(X260, bool), bool, 
125.30/125.53	               aa(X260, fun(fun(X260, bool), bool), member(X260), X262), 
125.30/125.53	               X261))),
125.30/125.53	    inference('cnf', [status(esa)], [fact_76_mem__def])).
125.30/125.53	tff('66', plain,
125.30/125.53	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
125.30/125.53	      (~ $true
125.30/125.53	       | ~ pp(
125.30/125.53	             aa(fun(X0, bool), bool, 
125.30/125.53	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))
125.30/125.53	       | pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))),
125.30/125.53	    inference('sup-', [status(thm)], ['64', '65'])).
125.30/125.53	tff('67', plain,
125.30/125.53	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool), X3 : X0]:
125.30/125.53	      (pp(aa(X0, bool, sup_sup(fun(X0, bool), X2, X1), X3))
125.30/125.53	       | ~ pp(
125.30/125.53	             aa(fun(X0, bool), bool, 
125.30/125.53	               aa(X0, fun(fun(X0, bool), bool), member(X0), X3), X2))),
125.30/125.53	    inference('simplify', [status(thm)], ['66'])).
125.30/125.53	tff('68', plain,
125.30/125.53	    ![X0 : fun(nat, bool)]:
125.30/125.53	      (~ $true
125.30/125.53	       | pp(
125.30/125.53	           aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
125.30/125.53	             aa(agent, nat, shrK, a)))),
125.30/125.53	    inference('sup-', [status(thm)], ['63', '67'])).
125.30/125.53	tff('69', plain,
125.30/125.53	    ![X0 : fun(nat, bool)]:
125.30/125.53	      pp(
125.30/125.53	        aa(nat, bool, sup_sup(fun(nat, bool), kk, X0), 
125.30/125.53	          aa(agent, nat, shrK, a))),
125.30/125.53	    inference('simplify', [status(thm)], ['68'])).
125.30/125.53	tff('70', plain,
125.30/125.53	    pp(
125.30/125.53	      aa(nat, bool, 
125.30/125.53	        uminus_uminus(fun(nat, bool), 
125.30/125.53	          image(agent, nat, shrK, top_top(fun(agent, bool)))), 
125.30/125.53	        aa(agent, nat, shrK, a))),
125.30/125.53	    inference('sup+', [status(thm)], ['9', '69'])).
125.30/125.53	tff(help_COMBB_1_1_U, axiom,
125.30/125.53	  (![C:$tType,B:$tType,A:$tType,R:A,Q:fun(A,B),P:fun(B,C)]:
125.30/125.53	     (aa(A,C,combb(B,C,A,P,Q),R) = aa(B,C,P,aa(A,B,Q,R))))).
125.30/125.53	tff('71', plain,
125.30/125.53	    ![X347 : $tType, X348 : $tType, X349 : fun(X347, X348), X350 : $tType, 
125.30/125.53	      X351 : fun(X350, X347), X352 : X350]:
125.30/125.53	      aa(X350, X348, combb(X347, X348, X350, X349, X351), X352)
125.30/125.53	       = aa(X347, X348, X349, aa(X350, X347, X351, X352)),
125.30/125.53	    inference('cnf', [status(esa)], [help_COMBB_1_1_U])).
125.30/125.53	tff(help_fNot_1_1_U, axiom,
125.30/125.53	  (![P:bool]: ((~pp(P)) | (~pp(aa(bool,bool,fNot,P)))))).
125.30/125.53	tff('72', plain,
125.30/125.53	    ![X345 : bool]: (~ pp(X345) | ~ pp(aa(bool, bool, fNot, X345))),
125.30/125.53	    inference('cnf', [status(esa)], [help_fNot_1_1_U])).
125.30/125.53	tff('73', plain,
125.30/125.53	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
125.30/125.53	      (~ pp(aa(X0, bool, combb(bool, bool, X0, fNot, X2), X1))
125.30/125.53	       | ~ pp(aa(X0, bool, X2, X1))),
125.30/125.53	    inference('sup-', [status(thm)], ['71', '72'])).
125.30/125.53	tff(fact_93_Collect__neg__eq, axiom,
125.30/125.53	  (![A:$tType,P1:fun(A,bool)]:
125.30/125.53	     (collect(A,combb(bool,bool,A,fNot,P1)) =
125.30/125.53	      uminus_uminus(fun(A,bool),collect(A,P1))))).
125.30/125.53	tff('74', plain,
125.30/125.53	    ![X310 : $tType, X311 : fun(X310, bool)]:
125.30/125.53	      collect(X310, combb(bool, bool, X310, fNot, X311))
125.30/125.53	       = uminus_uminus(fun(X310, bool), collect(X310, X311)),
125.30/125.53	    inference('cnf', [status(esa)], [fact_93_Collect__neg__eq])).
125.30/125.53	tff(fact_77_Collect__def, axiom,
125.30/125.53	  (![A:$tType,P1:fun(A,bool)]: (collect(A,P1) = P1))).
125.30/125.53	tff('75', plain,
125.30/125.53	    ![X264 : $tType, X265 : fun(X264, bool)]: collect(X264, X265) = X265,
125.30/125.53	    inference('cnf', [status(esa)], [fact_77_Collect__def])).
125.30/125.53	tff('76', plain,
125.30/125.53	    ![X310 : $tType, X311 : fun(X310, bool)]:
125.30/125.53	      combb(bool, bool, X310, fNot, X311)
125.30/125.53	       = uminus_uminus(fun(X310, bool), X311),
125.30/125.53	    inference('demod', [status(thm)], ['74', '75', '75'])).
125.30/125.53	tff('77', plain,
125.30/125.53	    ![X0 : $tType, X1 : X0, X2 : fun(X0, bool)]:
125.30/125.53	      (~ pp(aa(X0, bool, uminus_uminus(fun(X0, bool), X2), X1))
125.30/125.53	       | ~ pp(aa(X0, bool, X2, X1))),
125.30/125.53	    inference('demod', [status(thm)], ['73', '76'])).
125.30/125.53	tff('78', plain,
125.30/125.53	    (~ $true
125.30/125.53	     | ~ pp(
125.30/125.53	           aa(nat, bool, image(agent, nat, shrK, top_top(fun(agent, bool))), 
125.30/125.53	             aa(agent, nat, shrK, a)))),
125.30/125.53	    inference('sup-', [status(thm)], ['70', '77'])).
125.30/125.53	tff(help_COMBC_1_1_U, axiom,
125.30/125.53	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
125.30/125.53	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
125.30/125.53	tff('79', plain,
125.30/125.53	    ![X353 : $tType, X354 : $tType, X355 : $tType, 
125.30/125.53	      X356 : fun(X355, fun(X353, X354)), X357 : X355, X358 : X353]:
125.30/125.53	      aa(X355, X354, combc(X355, X353, X354, X356, X358), X357)
125.30/125.53	       = aa(X353, X354, aa(X355, fun(X353, X354), X356, X357), X358),
125.30/125.53	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
125.30/125.53	tff(fact_17_UNIV__I, axiom,
125.30/125.53	  (![A:$tType,X2:A]:
125.30/125.53	     pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),
125.30/125.53	           top_top(fun(A,bool)))))).
125.30/125.53	tff('80', plain,
125.30/125.53	    ![X48 : $tType, X49 : X48]:
125.30/125.53	      pp(
125.30/125.53	        aa(fun(X48, bool), bool, 
125.30/125.53	          aa(X48, fun(fun(X48, bool), bool), member(X48), X49), 
125.30/125.53	          top_top(fun(X48, bool)))),
125.30/125.53	    inference('cnf', [status(esa)], [fact_17_UNIV__I])).
125.30/125.53	tff(fact_16_image__eqI, axiom,
125.30/125.53	  (![A:$tType,B:$tType,A2:fun(B,bool),X2:B,F:fun(B,A),B3:A]:
125.30/125.53	     ((B3 = aa(B,A,F,X2)) =>
125.30/125.53	      (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2)) =>
125.30/125.53	       pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),B3),
125.30/125.53	             image(B,A,F,A2))))))).
125.30/125.53	tff('81', plain,
125.30/125.53	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
125.30/125.53	      X46 : fun(X42, X45), X47 : X45]:
125.30/125.53	      (~ pp(
125.30/125.53	           aa(fun(X42, bool), bool, 
125.30/125.53	             aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))
125.30/125.53	       | X47 != aa(X42, X45, X46, X43)
125.30/125.53	       | pp(
125.30/125.53	           aa(fun(X45, bool), bool, 
125.30/125.53	             aa(X45, fun(fun(X45, bool), bool), member(X45), X47), 
125.30/125.53	             image(X42, X45, X46, X44)))),
125.30/125.53	    inference('cnf', [status(esa)], [fact_16_image__eqI])).
125.30/125.53	tff('82', plain,
125.30/125.53	    ![X42 : $tType, X43 : X42, X44 : fun(X42, bool), X45 : $tType, 
125.30/125.53	      X46 : fun(X42, X45)]:
125.30/125.53	      (pp(
125.30/125.53	         aa(fun(X45, bool), bool, 
125.30/125.53	           aa(X45, fun(fun(X45, bool), bool), member(X45), 
125.30/125.53	             aa(X42, X45, X46, X43)), image(X42, X45, X46, X44)))
125.30/125.53	       | ~ pp(
125.30/125.53	             aa(fun(X42, bool), bool, 
125.30/125.53	               aa(X42, fun(fun(X42, bool), bool), member(X42), X43), X44))),
125.30/125.53	    inference('simplify', [status(thm)], ['81'])).
125.30/125.53	tff('83', plain,
125.30/125.53	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
125.30/125.53	      (~ $true
125.30/125.53	       | pp(
125.30/125.53	           aa(fun(X2, bool), bool, 
125.30/125.53	             aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
125.30/125.53	             image(X0, X2, X3, top_top(fun(X0, bool)))))),
125.30/125.53	    inference('sup-', [status(thm)], ['80', '82'])).
125.30/125.53	tff('84', plain,
125.30/125.53	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : fun(X0, X2)]:
125.30/125.53	      pp(
125.30/125.53	        aa(fun(X2, bool), bool, 
125.30/125.53	          aa(X2, fun(fun(X2, bool), bool), member(X2), aa(X0, X2, X3, X1)), 
125.30/125.53	          image(X0, X2, X3, top_top(fun(X0, bool))))),
125.30/125.53	    inference('simplify', [status(thm)], ['83'])).
125.30/125.53	tff('85', plain,
125.30/125.53	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
125.30/125.53	      pp(
125.30/125.53	        aa(X0, bool, 
125.30/125.53	          combc(X0, fun(X0, bool), bool, member(X0), 
125.30/125.53	            image(X1, X0, X3, top_top(fun(X1, bool)))), aa(X1, X0, X3, X2))),
125.30/125.53	    inference('sup+', [status(thm)], ['79', '84'])).
125.30/125.53	tff(fact_88_Compl__eq, axiom,
125.30/125.53	  (![A:$tType,A2:fun(A,bool)]:
125.30/125.53	     (uminus_uminus(fun(A,bool),A2) =
125.30/125.53	      collect(A,
125.30/125.53	              combb(bool,bool,A,fNot,combc(A,fun(A,bool),bool,member(A),A2)))))).
125.30/125.53	tff('86', plain,
125.30/125.53	    ![X295 : $tType, X296 : fun(X295, bool)]:
125.30/125.53	      uminus_uminus(fun(X295, bool), X296)
125.30/125.53	       = collect(X295, 
125.30/125.53	           combb(bool, bool, X295, fNot, 
125.30/125.53	             combc(X295, fun(X295, bool), bool, member(X295), X296))),
125.30/125.53	    inference('cnf', [status(esa)], [fact_88_Compl__eq])).
125.30/125.53	tff('87', plain,
125.30/125.53	    ![X295 : $tType, X296 : fun(X295, bool)]:
125.30/125.53	      uminus_uminus(fun(X295, bool), X296)
125.30/125.53	       = uminus_uminus(fun(X295, bool), 
125.30/125.53	           combc(X295, fun(X295, bool), bool, member(X295), X296)),
125.30/125.53	    inference('demod', [status(thm)], ['86', '76', '75'])).
125.30/125.53	tff(fact_87_double__complement, axiom,
125.30/125.53	  (![A:$tType,A2:fun(A,bool)]:
125.30/125.53	     (uminus_uminus(fun(A,bool),uminus_uminus(fun(A,bool),A2)) = A2))).
125.30/125.53	tff('88', plain,
125.30/125.53	    ![X293 : $tType, X294 : fun(X293, bool)]:
125.30/125.53	      uminus_uminus(fun(X293, bool), uminus_uminus(fun(X293, bool), X294))
125.30/125.53	       = X294,
125.30/125.53	    inference('cnf', [status(esa)], [fact_87_double__complement])).
125.30/125.53	tff('89', plain,
125.30/125.53	    ![X0 : $tType, X1 : fun(X0, bool)]:
125.30/125.53	      uminus_uminus(fun(X0, bool), uminus_uminus(fun(X0, bool), X1))
125.30/125.53	       = combc(X0, fun(X0, bool), bool, member(X0), X1),
125.30/125.53	    inference('sup+', [status(thm)], ['87', '88'])).
125.30/125.53	tff('90', plain,
125.30/125.53	    ![X0 : $tType, X1 : fun(X0, bool)]:
125.30/125.53	      X1 = combc(X0, fun(X0, bool), bool, member(X0), X1),
125.30/125.53	    inference('demod', [status(thm)], ['89', '88'])).
125.30/125.53	tff('91', plain,
125.30/125.53	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : fun(X1, X0)]:
125.30/125.53	      pp(
125.30/125.53	        aa(X0, bool, image(X1, X0, X3, top_top(fun(X1, bool))), 
125.30/125.53	          aa(X1, X0, X3, X2))),
125.30/125.53	    inference('demod', [status(thm)], ['85', '90'])).
125.30/125.53	tff('92', plain, (~ $true | ~ $true),
125.30/125.53	    inference('demod', [status(thm)], ['78', '91'])).
125.30/125.53	tff('93', plain, $false, inference('simplify', [status(thm)], ['92'])).
125.30/125.53	
125.30/125.53	% SZS output end Refutation
125.30/125.53	EOF
