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Ok?BPBSIBSQIF*IG*OIWUEUXXRVPAnswerIDPromptExpectedNotes
3
1
If the engine is on now, it will be on three states later.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
4
1
Whenever the engine is on, three states later the engine will be on.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
5
1
If the Engine is on in the current state, three states forward from now, the Engine must also be on - for this to be satisfied. Or the Engine could never be on.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
6
1
If the engine is on, the engine will be on 3 states from now
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
7
1
When the engine is on at a certain state, the engine will also be on 3 states after
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
8
1
If the engine is on, the engine will be on three states from now.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
9
1
If the engine is on, the 3rd state from that state will have the engine on.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
10
1
Always in all states, if the engine is on then three states later it should be on.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
11
1
If the engine is on, then the engine is on 3 states in the future.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
12
1
If the engine is on, it is on in the next of the next of the next state.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
13
1
Whenever the engine is on, the engine is also on 3 states later.
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Red implies after ( after ( after ( Red ) ) )
If Red initially, then Red again in 4th state.
14
1
From the third state onwards, eventually there will be a next state where the engine is on.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
15
1
After two states have passed, eventually the Engine after these the next state will be on.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
16
1
Three states from initial: from this point, the Engine must eventually turn on. If the Engine is on before the third state, it does not affect the satisfiability of the statement.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
17
1
sometime after two states from now, the next state will have the engine on
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
18
1
There will be a certain point where the engine is on, 2 states after the current state.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
19
1
After three states from now, the engine will eventually be on. \nOR\nAfter two states from now, the engine will eventually be on in the next state.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
20
1
There is a state such that in two states, there will eventually be a state such that the next state has the engine on.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
21
1
After two time steps, eventually the engine turns on.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
22
1
Starting 2 states from now, we will get to a state where the engine turns on in the next state.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
23
1
two states after the current state, there exists some state S that the engine is on in the next next of S.
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
24
1
From the third state on, at some point the engine will be on in s+1 following some state s (s >= 3).
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after ( after ( eventually ( after ( Red ) ) ) )
Red at 4th state or later
25
1
If at some point the engine turns on, then every state has the light on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
26
1
At some state in the future the Engine is on, and at that point the light will always be on after that state.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
27
1
If at any point the Engine turns on, the Light must be on throughout the entire trace. Otherwise, the Engine can be always off, and the trace satisfies the constraints.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
28
1
if the engine is turned on (or going to be turned on) at any state, the light is/was always on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
29
1
If the engine is on at a certain point after the current state, the light should always be on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
30
1
If the engine is on at some point, then the light is always on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
31
1
If the engine is on at some point during the trace, all states will have the lights on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
32
1
If the engine turns on, the light should always be on.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
33
1
If the engine eventually turns on, then the light is always on.
R_3s4jtgxJpj4seo8
{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
34
1
If the engine is on for some state, then the light is on for all states.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
35
1
If the engine is on in some state, this implies that the light will always be on in all states.
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{ eventually ( Red ) } implies { always ( Blue ) }
If ever Red, then Blue always from first state
36
11
The engine is always on, and since we engine until light, the light is never on.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
37
11
Engine is always on + light is never on at any point
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
38
1
The Engine must be on until the Light turns on, and the Engine must always be on. The Engine must always be on, and the Light can come on at some point and that trace will satisfy.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
39
1
the engine will be on until the light turns on, and the engine is always on
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
40
1
Engine is always on, light doesn't matter
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
41
1
The engine is always on, and the light eventually turns on.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
42
11
The engine will always be on and the light cannot turn on.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
43
1
Engine is always on and eventually the light turns on.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
44
1
If the light hasn't been turned on yet, the engine is on, and the engine is always on.
R_3s4jtgxJpj4seo8
( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
45
11
Engine is always on and light is never on because if the light is on then the engine should turn off.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
46
11
The engine will be on in all states before a light is ever on, and the engine will also always be on. This implies that the light will never be on, since the engine must always be on, and the engine can only be on until the light is on.
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( ( Red ) until ( Blue ) ) and always ( Red )
Red forever, Blue eventually
47
1
If the engine is on, then in the next state the engine is not on and two states later it turns back on.\nSo once the engine starts then it will alternate between on and off.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
48
1
If the engine is on at some state, the next state afterwards it is off, but two states afterwards the engine is again on.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
49
1
If the Engine ever turns on, it must turn on and off sequentially.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
50
1
if the engine is on in a given state, it must be off in the next state, and on in the next next state (engine alternates between being on and off)
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
51
1
For the entirety of the timeline, if a certain state has engine on, then the next state would not have engine on, but two states after the engine will be on.\n--> Engine will be on every other state, and off every other state, as long as there is engine somewhere
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
52
1
If the engine is on, the engine will be off in the next state, and then turn on again in the following state. (This forms an on-off cycle.)
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
53
1
At any point, if the engine is on, all future states will alternate between the engine being off and on.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
54
1
Once (not guaranteed) the engine turns on, it starts to alternate between turning on an off.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
55
1
For any state, if the engine is on: the engine has to be off for the next state, but has to be back on 2 states from now.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
56
1
For every state, If the engine is on, then it must be turned off in the next state, and it is on at two states after the current state.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
57
1
If the engine is on, then the engine is not on in the next state; the engine must be on, though, in the state following that.
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always ( Red implies ( after ( not Red ) and after ( after ( Red ) ) ) )
If Red then blinks forever
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