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LTLBench

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Initially, event3 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event1 can happen.

C1: Event3 happens and event2 happens. C2: C1 will happen at next time. C3: That event3 happens implies that C2 holds.

=== Context === Initially, event3 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event1 can happen. === Hypothesis === C1: Event3 happens and event2 happens. C2: C1 will happen at next time. C3: That event3 happens implies that C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event3 : event1; state = event2 : event2; state = event1 : event1; esac; LTLSPEC ((state=event3) -> (X ((state=event3) & (state=event2))))

(event3 -> (X (event3 & event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event2 can happen.

C1: That event3 happens implies that event1 happens. C2: That C1 holds implies that event3 happens. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: That event3 happens implies that event1 happens. C2: That C1 holds implies that event3 happens. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (X (((state=event3) -> (state=event1)) -> (state=event3)))

(X ((event3 -> event1) -> event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event1, event2 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event3 happens and event1 happens. C2: Event2 happens or C1 holds. C3: C2 will happen at next time.

=== Context === Initially, event2 happened. After event1, event2 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens and event1 happens. C2: Event2 happens or C1 holds. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (X ((state=event2) | ((state=event3) & (state=event1))))

(X (event2 | (event3 & event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event2 can happen.

C1: Event1 will always be true at any future time. C2: C1 does not hold. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: C1 does not hold. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (G (! (G (state=event1))))

(G (! (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event1, event3 can happen. After event3, event2 can happen. After event2, event1 can happen.

C1: Event1 will happen eventually. C2: C1 does not hold. C3: C2 will happen eventually.

=== Context === Initially, event3 happened. After event1, event3 can happen. After event3, event2 can happen. After event2, event1 can happen. === Hypothesis === C1: Event1 will happen eventually. C2: C1 does not hold. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event2; esac; LTLSPEC (F (! (F (state=event1))))

(F (! (F event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen.

C1: Event2 will always be true at any future time. C2: Event2 will always be true at any future time. C3: C1 holds and C2 holds.

=== Context === Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: Event2 will always be true at any future time. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC ((G (state=event2)) & (G (state=event2)))

((G event2) & (G event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event1 will always be true at any future time. C2: C1 does not hold. C3: C2 does not hold.

=== Context === Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: C1 does not hold. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event3; state = event3 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (! (! (G (state=event1))))

(! (! (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event1 will happen at next time. C2: Event2 happens or C1 holds. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: Event2 happens or C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event3 : event1; state = event3 : event2; state = event2 : event2; state = event1 : event1; esac; LTLSPEC (! ((state=event2) | (X (state=event1))))

(! (event2 | (X event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event3 can happen.

C1: Event3 will happen at next time. C2: C1 holds and event1 happens. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event3 will happen at next time. C2: C1 holds and event1 happens. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event3 : event2; state = event2 : event2; esac; LTLSPEC (X ((X (state=event3)) & (state=event1)))

(X ((X event3) & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 happens and event3 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 happens and event3 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (F (G ((state=event2) & (state=event3))))

(F (G (event2 & event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event2 can happen. After event2, no other events can happen. After event2, no other events can happen.

C1: Event1 happens or event1 happens. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time.

=== Context === Initially, event3 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event2 can happen. After event2, no other events can happen. After event2, no other events can happen. === Hypothesis === C1: Event1 happens or event1 happens. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event3 : event1; state = event3 : event2; state = event2 : event2; esac; LTLSPEC (G (G ((state=event1) | (state=event1))))

(G (G (event1 | event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 does not happen. C2: That event2 happens implies that C1 holds. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 does not happen. C2: That event2 happens implies that C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (! ((state=event2) -> (! (state=event2))))

(! (event2 -> (! event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event2 happens and event3 happens. C2: C1 will happen eventually. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 happens and event3 happens. C2: C1 will happen eventually. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event2; state = event2 : event2; esac; LTLSPEC (F (F ((state=event2) & (state=event3))))

(F (F (event2 & event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event2 can happen.

C1: Event2 will happen at next time. C2: C1 will happen eventually. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 will happen at next time. C2: C1 will happen eventually. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event3 : event2; state = event2 : event2; state = event1 : event1; esac; LTLSPEC (X (F (X (state=event2))))

(X (F (X event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event2 can happen.

C1: Event3 will happen at next time. C2: Event3 will happen at next time. C3: C1 holds and C2 holds.

=== Context === Initially, event3 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, event2 can happen. === Hypothesis === C1: Event3 will happen at next time. C2: Event3 will happen at next time. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event3 : event2; state = event2 : event2; esac; LTLSPEC ((X (state=event3)) & (X (state=event3)))

((X event3) & (X event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event2 can happen. After event2, event3 can happen. After event2, event3 can happen.

C1: Event1 will always be true at any future time. C2: C1 holds and event1 happens. C3: Event1 happens and C2 holds.

=== Context === Initially, event1 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event2 can happen. After event2, event3 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: C1 holds and event1 happens. C3: Event1 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC ((state=event1) & ((G (state=event1)) & (state=event1)))

(event1 & ((G event1) & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, no other events can happen.

C1: Event1 will happen at next time. C2: C1 holds or event2 happens. C3: That C2 holds implies that event2 happens.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, no other events can happen. === Hypothesis === C1: Event1 will happen at next time. C2: C1 holds or event2 happens. C3: That C2 holds implies that event2 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event3; state = event1 : event1; esac; LTLSPEC (((X (state=event1)) | (state=event2)) -> (state=event2))

(((X event1) | event2) -> event2)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event2 can happen.

C1: Event3 happens or event2 happens. C2: C1 holds and event3 happens. C3: C2 will always be true at any future time.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens or event2 happens. C2: C1 holds and event3 happens. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event2; esac; LTLSPEC (G (((state=event3) | (state=event2)) & (state=event3)))

(G ((event3 | event2) & event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event2 can happen.

C1: That event1 happens implies that event2 happens. C2: Event2 happens or C1 holds. C3: C2 does not hold.

=== Context === Initially, event3 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: That event1 happens implies that event2 happens. C2: Event2 happens or C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event2 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (! ((state=event2) | ((state=event1) -> (state=event2))))

(! (event2 | (event1 -> event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event3, no other events can happen. After event2, no other events can happen. After event1, event2 can happen.

C1: Event3 happens and event3 happens. C2: C1 does not hold. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event3, no other events can happen. After event2, no other events can happen. After event1, event2 can happen. === Hypothesis === C1: Event3 happens and event3 happens. C2: C1 does not hold. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event2; state = event3 : event3; esac; LTLSPEC (! (! ((state=event3) & (state=event3))))

(! (! (event3 & event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event1 can happen.

C1: Event1 will happen at next time. C2: Event1 will happen at next time. C3: C1 holds and C2 holds.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: Event1 will happen at next time. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC ((X (state=event1)) & (X (state=event1)))

((X event1) & (X event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, no other events can happen.

C1: Event3 happens and event3 happens. C2: That event2 happens implies that C1 holds. C3: Event3 happens and C2 holds.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 happens and event3 happens. C2: That event2 happens implies that C1 holds. C3: Event3 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event1; state = event3 : event3; state = event1 : event1; esac; LTLSPEC ((state=event3) & ((state=event2) -> ((state=event3) & (state=event3))))

(event3 & (event2 -> (event3 & event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, event3 can happen. After event3, no other events can happen. After event2, event1 can happen.

C1: Event1 does not happen. C2: C1 will happen at next time. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event1, event3 can happen. After event3, no other events can happen. After event2, event1 can happen. === Hypothesis === C1: Event1 does not happen. C2: C1 will happen at next time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event3; esac; LTLSPEC (G (X (! (state=event1))))

(G (X (! event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event1 will happen at next time. C2: C1 holds or event1 happens. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: C1 holds or event1 happens. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC (G ((X (state=event1)) | (state=event1)))

(G ((X event1) | event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event1 will always be true at any future time. C2: C1 will happen eventually. C3: Event2 happens and C2 holds.

=== Context === Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: C1 will happen eventually. C3: Event2 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event3 : event2; state = event2 : event2; esac; LTLSPEC ((state=event2) & (F (G (state=event1))))

(event2 & (F (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen.

C1: That event2 happens implies that event1 happens. C2: C1 does not hold. C3: C2 will happen at next time.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen. === Hypothesis === C1: That event2 happens implies that event1 happens. C2: C1 does not hold. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (X (! ((state=event2) -> (state=event1))))

(X (! (event2 -> event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen.

C1: Event2 will happen at next time. C2: C1 will happen at next time. C3: C2 will happen eventually.

=== Context === Initially, event2 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen. === Hypothesis === C1: Event2 will happen at next time. C2: C1 will happen at next time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC (F (X (X (state=event2))))

(F (X (X event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, event2 can happen. After event2, event3 can happen. After event3, no other events can happen.

C1: Event3 happens or event2 happens. C2: C1 holds or event3 happens. C3: C2 does not hold.

=== Context === Initially, event2 happened. After event1, event2 can happen. After event2, event3 can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 happens or event2 happens. C2: C1 holds or event3 happens. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (! (((state=event3) | (state=event2)) | (state=event3)))

(! ((event3 | event2) | event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event1 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen.

C1: Event2 happens or event2 happens. C2: C1 will happen at next time. C3: C2 holds and event2 happens.

=== Context === Initially, event1 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. === Hypothesis === C1: Event2 happens or event2 happens. C2: C1 will happen at next time. C3: C2 holds and event2 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC ((X ((state=event2) | (state=event2))) & (state=event2))

((X (event2 | event2)) & event2)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event3 can happen. After event3, event2 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event3 happens or event2 happens. C2: Event3 happens and C1 holds. C3: C2 holds or event3 happens.

=== Context === Initially, event1 happened. After event2, event3 can happen. After event3, event2 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event3 happens or event2 happens. C2: Event3 happens and C1 holds. C3: C2 holds or event3 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event2; esac; LTLSPEC (((state=event3) & ((state=event3) | (state=event2))) | (state=event3))

((event3 & (event3 | event2)) | event3)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, no other events can happen.

C1: That event2 happens implies that event1 happens. C2: C1 will happen at next time. C3: C2 holds and event3 happens.

=== Context === Initially, event1 happened. After event2, no other events can happen. After event3, event2 can happen. After event1, no other events can happen. === Hypothesis === C1: That event2 happens implies that event1 happens. C2: C1 will happen at next time. C3: C2 holds and event3 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event3 : event2; state = event2 : event2; state = event1 : event1; esac; LTLSPEC ((X ((state=event2) -> (state=event1))) & (state=event3))

((X (event2 -> event1)) & event3)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event3, no other events can happen. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event1 will happen at next time. C2: Event1 will happen at next time. C3: C1 holds or C2 holds.

=== Context === Initially, event1 happened. After event3, no other events can happen. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: Event1 will happen at next time. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event3 : event3; esac; LTLSPEC ((X (state=event1)) | (X (state=event1)))

((X event1) | (X event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event3, no other events can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event2 happens or event1 happens. C2: Event2 happens and C1 holds. C3: C2 will happen at next time.

=== Context === Initially, event3 happened. After event3, no other events can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 happens or event1 happens. C2: Event2 happens and C1 holds. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (X ((state=event2) & ((state=event2) | (state=event1))))

(X (event2 & (event2 | event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event3 does not happen. C2: C1 holds and event3 happens. C3: C2 holds and event1 happens.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 does not happen. C2: C1 holds and event3 happens. C3: C2 holds and event1 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (((! (state=event3)) & (state=event3)) & (state=event1))

(((! event3) & event3) & event1)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen.

C1: That event3 happens implies that event3 happens. C2: Event2 happens and C1 holds. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. === Hypothesis === C1: That event3 happens implies that event3 happens. C2: Event2 happens and C1 holds. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (G ((state=event2) & ((state=event3) -> (state=event3))))

(G (event2 & (event3 -> event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen.

C1: Event2 happens and event2 happens. C2: C1 will happen at next time. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen. === Hypothesis === C1: Event2 happens and event2 happens. C2: C1 will happen at next time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (G (X ((state=event2) & (state=event2))))

(G (X (event2 & event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, no other events can happen.

C1: That event3 happens implies that event3 happens. C2: C1 does not hold. C3: C2 will happen eventually.

=== Context === Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, no other events can happen. === Hypothesis === C1: That event3 happens implies that event3 happens. C2: C1 does not hold. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event2 : event2; state = event3 : event3; state = event1 : event1; esac; LTLSPEC (F (! ((state=event3) -> (state=event3))))

(F (! (event3 -> event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 will happen eventually. C2: C1 will always be true at any future time. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 will happen eventually. C2: C1 will always be true at any future time. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (X (G (F (state=event2))))

(X (G (F event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event1 can happen.

C1: Event1 will always be true at any future time. C2: C1 will happen eventually. C3: C2 does not hold.

=== Context === Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: C1 will happen eventually. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event3; state = event3 : event1; state = event1 : event1; esac; LTLSPEC (! (F (G (state=event1))))

(! (F (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event2 can happen.

C1: Event1 happens or event1 happens. C2: C1 does not hold. C3: Event1 happens and C2 holds.

=== Context === Initially, event2 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 happens or event1 happens. C2: C1 does not hold. C3: Event1 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event3; state = event3 : event2; state = event1 : event1; esac; LTLSPEC ((state=event1) & (! ((state=event1) | (state=event1))))

(event1 & (! (event1 | event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event3 happens and event2 happens. C2: C1 will happen at next time. C3: Event2 happens and C2 holds.

=== Context === Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 happens and event2 happens. C2: C1 will happen at next time. C3: Event2 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event3; esac; LTLSPEC ((state=event2) & (X ((state=event3) & (state=event2))))

(event2 & (X (event3 & event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 will happen eventually. C2: C1 does not hold. C3: C2 will happen at next time.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 will happen eventually. C2: C1 does not hold. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (X (! (F (state=event2))))

(X (! (F event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, no other events can happen.

C1: Event2 will happen at next time. C2: C1 will happen at next time. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 will happen at next time. C2: C1 will happen at next time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event2 : event3; state = event3 : event3; state = event1 : event1; esac; LTLSPEC (F (X (X (state=event2))))

(F (X (X event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event3 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen.

C1: Event2 will happen eventually. C2: C1 holds or event2 happens. C3: Event1 happens or C2 holds.

=== Context === Initially, event3 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen. === Hypothesis === C1: Event2 will happen eventually. C2: C1 holds or event2 happens. C3: Event1 happens or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC ((state=event1) | ((F (state=event2)) | (state=event2)))

(event1 | ((F event2) | event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, no other events can happen.

C1: That event2 happens implies that event1 happens. C2: C1 holds or event1 happens. C3: Event2 happens and C2 holds.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, no other events can happen. === Hypothesis === C1: That event2 happens implies that event1 happens. C2: C1 holds or event1 happens. C3: Event2 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event3; esac; LTLSPEC ((state=event2) & (((state=event2) -> (state=event1)) | (state=event1)))

(event2 & ((event2 -> event1) | event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event2 can happen.

C1: Event3 happens and event3 happens. C2: Event3 happens and event3 happens. C3: C1 holds and C2 holds.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens and event3 happens. C2: Event3 happens and event3 happens. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (((state=event3) & (state=event3)) & ((state=event3) & (state=event3)))

((event3 & event3) & (event3 & event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 happens and event3 happens. C2: C1 holds and event1 happens. C3: That event1 happens implies that C2 holds.

=== Context === Initially, event1 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 happens and event3 happens. C2: C1 holds and event1 happens. C3: That event1 happens implies that C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC ((state=event1) -> (((state=event2) & (state=event3)) & (state=event1)))

(event1 -> ((event2 & event3) & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen.

C1: Event2 will happen at next time. C2: That C1 holds implies that event1 happens. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen. === Hypothesis === C1: Event2 will happen at next time. C2: That C1 holds implies that event1 happens. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC (! ((X (state=event2)) -> (state=event1)))

(! ((X event2) -> event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen.

C1: Event1 will happen at next time. C2: C1 will happen eventually. C3: C2 will happen at next time.

=== Context === Initially, event2 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: C1 will happen eventually. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event3 : event1; state = event2 : event2; esac; LTLSPEC (X (F (X (state=event1))))

(X (F (X event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event1, no other events can happen. After event2, event3 can happen.

C1: Event1 does not happen. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event1, no other events can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 does not happen. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event3; state = event3 : event1; state = event1 : event1; esac; LTLSPEC (G (G (! (state=event1))))

(G (G (! event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, event3 can happen.

C1: Event2 happens and event1 happens. C2: C1 will happen eventually. C3: C2 will happen at next time.

=== Context === Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 happens and event1 happens. C2: C1 will happen eventually. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event2; state = event3 : event3; esac; LTLSPEC (X (F ((state=event2) & (state=event1))))

(X (F (event2 & event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event2 will happen at next time. C2: C1 will always be true at any future time. C3: C2 holds or event2 happens.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 will happen at next time. C2: C1 will always be true at any future time. C3: C2 holds or event2 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC ((G (X (state=event2))) | (state=event2))

((G (X event2)) | event2)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event2 will always be true at any future time. C2: C1 will happen eventually. C3: Event3 happens and C2 holds.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: C1 will happen eventually. C3: Event3 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event1; state = event3 : event2; esac; LTLSPEC ((state=event3) & (F (G (state=event2))))

(event3 & (F (G event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, event3 can happen.

C1: Event2 will happen eventually. C2: C1 will happen at next time. C3: C2 will happen at next time.

=== Context === Initially, event3 happened. After event2, no other events can happen. After event3, no other events can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 will happen eventually. C2: C1 will happen at next time. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event2; state = event3 : event3; esac; LTLSPEC (X (X (F (state=event2))))

(X (X (F event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> </graph> </graphml>

Initially, event3 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event3 happens and event1 happens. C2: C1 will happen eventually. C3: Event3 happens and C2 holds.

=== Context === Initially, event3 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens and event1 happens. C2: C1 will happen eventually. C3: Event3 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC ((state=event3) & (F ((state=event3) & (state=event1))))

(event3 & (F (event3 & event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event3 can happen.

C1: Event1 will happen at next time. C2: C1 will happen at next time. C3: C2 holds and event3 happens.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 will happen at next time. C2: C1 will happen at next time. C3: C2 holds and event3 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event3; state = event3 : event1; esac; LTLSPEC ((X (X (state=event1))) & (state=event3))

((X (X event1)) & event3)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event1 can happen.

C1: Event1 happens or event1 happens. C2: C1 will happen eventually. C3: Event3 happens and C2 holds.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, no other events can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 happens or event1 happens. C2: C1 will happen eventually. C3: Event3 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event1; state = event1 : event1; esac; LTLSPEC ((state=event3) & (F ((state=event1) | (state=event1))))

(event3 & (F (event1 | event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event3 can happen. After event3, no other events can happen. After event1, event3 can happen.

C1: Event2 will always be true at any future time. C2: Event1 happens or C1 holds. C3: C2 will always be true at any future time.

=== Context === Initially, event1 happened. After event2, event3 can happen. After event3, no other events can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: Event1 happens or C1 holds. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (G ((state=event1) | (G (state=event2))))

(G (event1 | (G event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event2, event3 can happen. After event3, event2 can happen. After event1, no other events can happen.

C1: Event2 happens and event1 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually.

=== Context === Initially, event2 happened. After event2, event3 can happen. After event3, event2 can happen. After event1, no other events can happen. === Hypothesis === C1: Event2 happens and event1 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event3; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (F (G ((state=event2) & (state=event1))))

(F (G (event2 & event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event1, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event1 will happen eventually. C2: C1 holds or event1 happens. C3: C2 does not hold.

=== Context === Initially, event3 happened. After event1, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 will happen eventually. C2: C1 holds or event1 happens. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event2 : event1; state = event2 : event3; state = event3 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (! ((F (state=event1)) | (state=event1)))

(! ((F event1) | event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event3 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen.

C1: Event3 does not happen. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time.

=== Context === Initially, event3 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen. === Hypothesis === C1: Event3 does not happen. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC (G (G (! (state=event3))))

(G (G (! event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event3 can happen.

C1: Event2 will always be true at any future time. C2: Event2 will always be true at any future time. C3: C1 holds or C2 holds.

=== Context === Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event3 can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: Event2 will always be true at any future time. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event3; state = event3 : event1; esac; LTLSPEC ((G (state=event2)) | (G (state=event2)))

((G event2) | (G event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event2 can happen.

C1: Event3 happens or event3 happens. C2: Event3 happens or event3 happens. C3: C1 holds or C2 holds.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens or event3 happens. C2: Event3 happens or event3 happens. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event2; esac; LTLSPEC (((state=event3) | (state=event3)) | ((state=event3) | (state=event3)))

((event3 | event3) | (event3 | event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event2 will always be true at any future time. C2: C1 holds or event3 happens. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: C1 holds or event3 happens. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (F ((G (state=event2)) | (state=event3)))

(F ((G event2) | event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen.

C1: Event1 happens or event2 happens. C2: That C1 holds implies that event2 happens. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 happens or event2 happens. C2: That C1 holds implies that event2 happens. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (G (((state=event1) | (state=event2)) -> (state=event2)))

(G ((event1 | event2) -> event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event3, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event3 happens and event3 happens. C2: Event3 happens and event3 happens. C3: C1 holds or C2 holds.

=== Context === Initially, event2 happened. After event3, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event3 happens and event3 happens. C2: Event3 happens and event3 happens. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event2; esac; LTLSPEC (((state=event3) & (state=event3)) | ((state=event3) & (state=event3)))

((event3 & event3) | (event3 & event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event3, event2 can happen. After event2, event1 can happen. After event1, no other events can happen.

C1: Event1 will always be true at any future time. C2: Event1 happens or C1 holds. C3: C2 holds or event1 happens.

=== Context === Initially, event2 happened. After event3, event2 can happen. After event2, event1 can happen. After event1, no other events can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: Event1 happens or C1 holds. C3: C2 holds or event1 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (((state=event1) | (G (state=event1))) | (state=event1))

((event1 | (G event1)) | event1)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, no other events can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event3 happens or event3 happens. C2: That event1 happens implies that C1 holds. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, no other events can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 happens or event3 happens. C2: That event1 happens implies that C1 holds. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event2 : event1; state = event2 : event3; state = event3 : event1; state = event3 : event2; state = event1 : event1; esac; LTLSPEC (G ((state=event1) -> ((state=event3) | (state=event3))))

(G (event1 -> (event3 | event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event2, event1 can happen. After event2, event3 can happen.

C1: Event1 does not happen. C2: C1 does not hold. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event1, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 does not happen. C2: C1 does not hold. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (! (! (! (state=event1))))

(! (! (! event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen.

C1: Event1 will always be true at any future time. C2: Event1 will always be true at any future time. C3: C1 holds or C2 holds.

=== Context === Initially, event2 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, no other events can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: Event1 will always be true at any future time. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC ((G (state=event1)) | (G (state=event1)))

((G event1) | (G event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen.

C1: Event2 does not happen. C2: C1 does not hold. C3: C2 holds and event2 happens.

=== Context === Initially, event1 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event2 does not happen. C2: C1 does not hold. C3: C2 holds and event2 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC ((! (! (state=event2))) & (state=event2))

((! (! event2)) & event2)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen.

C1: Event1 will always be true at any future time. C2: Event1 will always be true at any future time. C3: C1 holds and C2 holds.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: Event1 will always be true at any future time. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC ((G (state=event1)) & (G (state=event1)))

((G event1) & (G event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event2 can happen.

C1: Event3 will happen at next time. C2: C1 holds and event3 happens. C3: C2 will happen eventually.

=== Context === Initially, event3 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event2 can happen. === Hypothesis === C1: Event3 will happen at next time. C2: C1 holds and event3 happens. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (F ((X (state=event3)) & (state=event3)))

(F ((X event3) & event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, no other events can happen.

C1: Event2 will happen eventually. C2: C1 holds or event1 happens. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, no other events can happen. === Hypothesis === C1: Event2 will happen eventually. C2: C1 holds or event1 happens. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event3; state = event3 : event1; state = event1 : event1; esac; LTLSPEC (! ((F (state=event2)) | (state=event1)))

(! ((F event2) | event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event1 will happen eventually. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event1 will happen eventually. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (G (G (F (state=event1))))

(G (G (F event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event1 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen.

C1: Event1 happens and event2 happens. C2: C1 holds and event1 happens. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. After event3, event2 can happen. === Hypothesis === C1: Event1 happens and event2 happens. C2: C1 holds and event1 happens. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event2 : event1; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (X (((state=event1) & (state=event2)) & (state=event1)))

(X ((event1 & event2) & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen.

C1: Event1 does not happen. C2: Event1 does not happen. C3: C1 holds or C2 holds.

=== Context === Initially, event1 happened. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 does not happen. C2: Event1 does not happen. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event3; state = event3 : event1; esac; LTLSPEC ((! (state=event1)) | (! (state=event1)))

((! event1) | (! event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event1 can happen.

C1: Event3 will always be true at any future time. C2: That C1 holds implies that event2 happens. C3: Event2 happens and C2 holds.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event1, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event3 will always be true at any future time. C2: That C1 holds implies that event2 happens. C3: Event2 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC ((state=event2) & ((G (state=event3)) -> (state=event2)))

(event2 & ((G event3) -> event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, no other events can happen.

C1: Event1 will happen at next time. C2: That event2 happens implies that C1 holds. C3: C2 does not hold.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event3, no other events can happen. === Hypothesis === C1: Event1 will happen at next time. C2: That event2 happens implies that C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event1; state = event3 : event3; esac; LTLSPEC (! ((state=event2) -> (X (state=event1))))

(! (event2 -> (X event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen.

C1: Event1 will always be true at any future time. C2: That event2 happens implies that C1 holds. C3: C2 does not hold.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: That event2 happens implies that C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC (! ((state=event2) -> (G (state=event1))))

(! (event2 -> (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen. After event2, event3 can happen.

C1: Event1 will always be true at any future time. C2: Event3 happens or C1 holds. C3: C2 will always be true at any future time.

=== Context === Initially, event3 happened. After event1, event3 can happen. After event3, event1 can happen. After event2, event1 can happen. After event2, event3 can happen. === Hypothesis === C1: Event1 will always be true at any future time. C2: Event3 happens or C1 holds. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (G ((state=event3) | (G (state=event1))))

(G (event3 | (G event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen.

C1: Event2 happens and event2 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event3, event1 can happen. After event1, event3 can happen. After event2, event1 can happen. === Hypothesis === C1: Event2 happens and event2 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event3 : event1; esac; LTLSPEC (F (G ((state=event2) & (state=event2))))

(F (G (event2 & event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen.

C1: Event2 happens or event3 happens. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time.

=== Context === Initially, event3 happened. After event1, event2 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, event1 can happen. === Hypothesis === C1: Event2 happens or event3 happens. C2: C1 will always be true at any future time. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (G (G ((state=event2) | (state=event3))))

(G (G (event2 | event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, no other events can happen.

C1: Event3 does not happen. C2: C1 will always be true at any future time. C3: C2 will happen eventually.

=== Context === Initially, event3 happened. After event1, no other events can happen. After event2, event3 can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 does not happen. C2: C1 will always be true at any future time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event2 : event3; state = event3 : event3; state = event1 : event1; esac; LTLSPEC (F (G (! (state=event3))))

(F (G (! event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen.

C1: Event1 happens and event3 happens. C2: C1 will happen at next time. C3: C2 will happen at next time.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen. After event3, event1 can happen. After event3, event1 can happen. === Hypothesis === C1: Event1 happens and event3 happens. C2: C1 will happen at next time. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (X (X ((state=event1) & (state=event3))))

(X (X (event1 & event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event3 can happen.

C1: Event2 does not happen. C2: C1 holds and event1 happens. C3: C2 will always be true at any future time.

=== Context === Initially, event1 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 does not happen. C2: C1 holds and event1 happens. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC (G ((! (state=event2)) & (state=event1)))

(G ((! event2) & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event3, event2 can happen. After event2, no other events can happen. After event1, event3 can happen.

C1: Event2 will happen at next time. C2: C1 does not hold. C3: C2 does not hold.

=== Context === Initially, event1 happened. After event3, event2 can happen. After event2, no other events can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 will happen at next time. C2: C1 does not hold. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event3 : event2; state = event2 : event2; esac; LTLSPEC (! (! (X (state=event2))))

(! (! (X event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event1 can happen.

C1: Event3 happens and event2 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually.

=== Context === Initially, event1 happened. After event1, no other events can happen. After event2, event1 can happen. After event3, event1 can happen. === Hypothesis === C1: Event3 happens and event2 happens. C2: C1 will always be true at any future time. C3: C2 will happen eventually. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event2 : event1; state = event3 : event1; state = event1 : event1; esac; LTLSPEC (F (G ((state=event3) & (state=event2))))

(F (G (event3 & event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event2" target="event1" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event2 can happen.

C1: Event2 does not happen. C2: That event2 happens implies that C1 holds. C3: C2 does not hold.

=== Context === Initially, event3 happened. After event1, no other events can happen. After event2, no other events can happen. After event3, event2 can happen. === Hypothesis === C1: Event2 does not happen. C2: That event2 happens implies that C1 holds. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event3 : event2; state = event2 : event2; state = event1 : event1; esac; LTLSPEC (! ((state=event2) -> (! (state=event2))))

(! (event2 -> (! event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event3 can happen. After event2, event3 can happen.

C1: Event2 happens or event2 happens. C2: C1 will happen eventually. C3: C2 will happen at next time.

=== Context === Initially, event2 happened. After event3, event1 can happen. After event3, event2 can happen. After event1, event3 can happen. After event2, event3 can happen. === Hypothesis === C1: Event2 happens or event2 happens. C2: C1 will happen eventually. C3: C2 will happen at next time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event3; state = event3 : event1; state = event3 : event2; esac; LTLSPEC (X (F ((state=event2) | (state=event2))))

(X (F (event2 | event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen.

C1: Event2 will always be true at any future time. C2: C1 will happen at next time. C3: That event1 happens implies that C2 holds.

=== Context === Initially, event1 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 will always be true at any future time. C2: C1 will happen at next time. C3: That event1 happens implies that C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event3 : event3; esac; LTLSPEC ((state=event1) -> (X (G (state=event2))))

(event1 -> (X (G event2)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event3, no other events can happen.

C1: Event2 will happen at next time. C2: That event2 happens implies that C1 holds. C3: C2 holds and event2 happens.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 will happen at next time. C2: That event2 happens implies that C1 holds. C3: C2 holds and event2 happens. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (((state=event2) -> (X (state=event2))) & (state=event2))

((event2 -> (X event2)) & event2)

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event2 can happen.

C1: Event3 happens or event3 happens. C2: Event3 happens or event3 happens. C3: C1 holds and C2 holds.

=== Context === Initially, event2 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event2 can happen. === Hypothesis === C1: Event3 happens or event3 happens. C2: Event3 happens or event3 happens. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (((state=event3) | (state=event3)) & ((state=event3) | (state=event3)))

((event3 | event3) & (event3 | event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event1 happened. After event3, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen.

C1: Event3 will happen at next time. C2: C1 will happen at next time. C3: Event3 happens and C2 holds.

=== Context === Initially, event1 happened. After event3, no other events can happen. After event2, event1 can happen. After event2, event3 can happen. After event1, event3 can happen. === Hypothesis === C1: Event3 will happen at next time. C2: C1 will happen at next time. C3: Event3 happens and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC ((state=event3) & (X (X (state=event3))))

(event3 & (X (X event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event3 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, no other events can happen. After event3, no other events can happen.

C1: Event2 happens and event3 happens. C2: Event2 happens and event3 happens. C3: C1 holds and C2 holds.

=== Context === Initially, event3 happened. After event1, event2 can happen. After event1, event3 can happen. After event2, event1 can happen. After event2, event3 can happen. After event3, no other events can happen. After event3, no other events can happen. === Hypothesis === C1: Event2 happens and event3 happens. C2: Event2 happens and event3 happens. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (((state=event2) & (state=event3)) & ((state=event2) & (state=event3)))

((event2 & event3) & (event2 & event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event1 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen.

C1: Event2 happens and event2 happens. C2: Event2 happens and event2 happens. C3: C1 holds and C2 holds.

=== Context === Initially, event1 happened. After event2, no other events can happen. After event3, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. === Hypothesis === C1: Event2 happens and event2 happens. C2: Event2 happens and event2 happens. C3: C1 holds and C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event1; next(state) := case state = event1 : event2; state = event1 : event3; state = event3 : event1; state = event2 : event2; esac; LTLSPEC (((state=event2) & (state=event2)) & ((state=event2) & (state=event2)))

((event2 & event2) & (event2 & event2))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event2 can happen. After event3, event2 can happen.

C1: Event3 will always be true at any future time. C2: That event3 happens implies that C1 holds. C3: C2 will always be true at any future time.

=== Context === Initially, event3 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, event2 can happen. After event3, event2 can happen. === Hypothesis === C1: Event3 will always be true at any future time. C2: That event3 happens implies that C1 holds. C3: C2 will always be true at any future time. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event3; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event2 : event3; state = event3 : event2; esac; LTLSPEC (G ((state=event3) -> (G (state=event3))))

(G (event3 -> (G event3)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> <edge source="event3" target="event2" /> </graph> </graphml>

Initially, event2 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event3 can happen.

C1: Event3 happens and event1 happens. C2: Event3 happens and event1 happens. C3: C1 holds or C2 holds.

=== Context === Initially, event2 happened. After event2, event3 can happen. After event3, event1 can happen. After event1, event3 can happen. === Hypothesis === C1: Event3 happens and event1 happens. C2: Event3 happens and event1 happens. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event3; state = event2 : event3; state = event3 : event1; esac; LTLSPEC (((state=event3) & (state=event1)) | ((state=event3) & (state=event1)))

((event3 & event1) | (event3 & event1))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event3" /> <edge source="event2" target="event3" /> <edge source="event3" target="event1" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event3, no other events can happen.

C1: That event3 happens implies that event1 happens. C2: C1 will happen eventually. C3: C2 does not hold.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event2, event3 can happen. After event1, event2 can happen. After event3, no other events can happen. === Hypothesis === C1: That event3 happens implies that event1 happens. C2: C1 will happen eventually. C3: C2 does not hold. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event2 : event1; state = event2 : event3; state = event3 : event3; esac; LTLSPEC (! (F ((state=event3) -> (state=event1))))

(! (F (event3 -> event1)))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event2" target="event1" /> <edge source="event2" target="event3" /> </graph> </graphml>

Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen.

C1: Event3 will happen eventually. C2: Event3 will happen eventually. C3: C1 holds or C2 holds.

=== Context === Initially, event2 happened. After event2, event1 can happen. After event1, event2 can happen. After event1, event3 can happen. After event3, no other events can happen. === Hypothesis === C1: Event3 will happen eventually. C2: Event3 will happen eventually. C3: C1 holds or C2 holds. C3 is True or False? Answer with "True" or "False" directly:

MODULE main VAR state : {event1, event2, event3}; ASSIGN init(state) := event2; next(state) := case state = event1 : event2; state = event1 : event3; state = event2 : event1; state = event3 : event3; esac; LTLSPEC ((F (state=event3)) | (F (state=event3)))

((F event3) | (F event3))

<graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd"> <graph edgedefault="directed"> <node id="event1" /> <node id="event2" /> <node id="event3" /> <edge source="event1" target="event2" /> <edge source="event1" target="event3" /> <edge source="event2" target="event1" /> </graph> </graphml>