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spot/bench/emptchk/formulae.ltl
Alexandre Duret-Lutz fdf8878db3 Update formulae.ltl not to use uncommon operators. 
* bench/emptchk/formulae.ltl: Do not use + and * in the list of
formulas.  Use | and & instead.  The * operator was removed on
2010-01-30.  Reported by Étienne Renault.
2011-11-24 22:03:42 +01:00

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p0 U (p1 & G p2)
p0 U (p1 & X (p2 U p3))
p0 U (p1 & (X (p2 & (F (p3 & (X (F (p4 & X (F (p5 & (X (F p6))))))))))))
F (p0 & XGp1)
F (p0 & X (p1 & XFp2))
F (p0 & X (p1 U p2))
FGp0 | FGp1
G (!p0 | (p1 U p2))
F (p0 & (XF (p1 & XF (p2 & XF p3))))
GFp0 & GFp1 & GFp2 & GFp3 & GFp4
(p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1))
G (! p0 | (p1 U (G p2 | G p3)))
p=1Uq=1
p=1U(q=1Ur=1)
!(p=1U(q=1Ur=1))
G(F(p=1))->G(F(q=1))
F(p=1)UG(q=1)
G(p=1)Uq=1
!(F(F(p=1))<->F(p=1))
!(G(F(p=1))->G(F(q=1)))
G(F(p=1))^G(F(q=1))
p=1R(p=1|q=1)
(X(p=1)UX(q=1))|!X(p=1Uq=1)
(X(p=1)Uq=1)|!X(p=1U(p=1&q=1))
G(p=1->F(q=1))&((X(p=1)Uq=1)|!X(p=1U(p=1&q=1)))
G(p=1->F(q=1))&((X(p=1)UX(q=1))|!X(p=1Uq=1))
G(p=1->F(q=1))
!G(p=1->X(q=1Rr=1))
!(G(F(p=1))|F(G(q=1)))
G(F(p=1)&F(q=1))
F(p=1)&F(p=0)
((X(q=0))&(r=0))R(X((((s=0)U(p=0))R(r=0))U((s=0)R(r=0))))
(G(q=1|G(F(p=1)))&G(r=1|G(F(p=0))))|G(q=1)|G(r=1)
(G(q=1|F(G(p=1)))&G(r=1|F(G(p=0))))|G(q=1)|G(r=1)
!((G(q=1|G(F(p=1)))&G(r=1|G(F(p=0))))|G(q=1)|G(r=1))
!((G(q=1|F(G(p=1)))&G(r=1|F(G(p=0))))|G(q=1)|G(r=1))
G(q=1|X(G(p=1)))&G(r=1|X(G(p=0)))
G(p=1|(X(q=1)&X(q=0)))
(p=1Uq=1)|(q=1Up=1)
[](!a)
<>b -> (!a U b)
[](c -> [](!a))
[]((c & !b & <>b) -> (!a U b))
[](c & !b -> (!a U (b | []!a)))
<>(a)
!b U ((a & !b) | []!b)
[](!c) | <>(c & <>a)
[](c & !b -> (!b U ((a & !b) | []!b)))
[](c & !b -> (!b U (a & !b)))
<>b -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U b)))))))))
[]((c & <>b) -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U b))))))))))
[](c -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U (b | []!a)) | []a)))))))))
[](a)
<>b -> (a U b)
[](c -> [](a))
[]((c & !b & <>b) -> (a U b))
[](c & !b -> (a U (b | [] a)))
!a U (d | []!a)
<>b -> (!a U (d | b))
[]!c | <>(c & (!a U (d | []!a)))
[]((c & !b & <>b) -> (!a U (d | b)))
[](c & !b -> (!a U ((d | b) | []!a)))
[](a -> <>d)
<>b -> (a -> (!b U (d & !b))) U b
[](c -> [](a -> <>d))
[]((c & !b & <>b) -> (a -> (!b U (d & !b))) U b)
[](c & !b -> ((a -> (!b U (d & !b))) U (b | [](a -> (!b U (d & !b))))))
<>a -> (!a U (d & !a & X(!a U e)))
<>b -> (!a U (b | (d & !a & X(!a U e))))
([]!c) | (!c U (c & <>a -> (!a U (d & !a & X(!a U e)))))
[]((c & <>b) -> (!a U (b | (d & !a & X(!a U e)))))
[](c -> (<>a -> (!a U (b | (d & !a & X(!a U e))))))
(<>(d & X<>e)) -> ((!d) U a)
<>b -> ((!(d & (!b) & X(!b U (e & !b)))) U (b | a))
([]!c) | ((!c) U (c & ((<>(d & X<>e)) -> ((!d) U a))))
[]((c & <>b) -> ((!(d & (!b) & X(!b U (e & !b)))) U (b | a)))
[](c -> (!(d & (!b) & X(!b U (e & !b))) U (b | a) | [](!(d & X<>e))))
[] (d & X<> e -> X(<>(e & <> a)))
<>b -> (d & X(!b U e) -> X(!b U (e & <> a))) U b
[] (c -> [] (d & X<> e -> X(!e U (e & <> a))))
[] ((c & <>b) -> (d & X(!b U e) -> X(!b U (e & <> a))) U b)
[] (c -> (d & X(!b U e) -> X(!b U (e & <> a))) U (b | [] (d & X(!b U e) -> X(!b U (e & <> a)))))
[] (a -> <>(d & X<>e))
<>b -> (a -> (!b U (d & !b & X(!b U e)))) U b
[] (c -> [] (a -> (d & X<> e)))
[] ((c & <>b) -> (a -> (!b U (d & !b & X(!b U e)))) U b)
[] (c -> (a -> (!b U (d & !b & X(!b U e)))) U (b | [] (a -> (d & X<> e))))
[] (a -> <>(d & !f & X(!f U e)))
<>b -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U b
[] (c -> [] (a -> (d & !f & X(!f U e))))
[] ((c & <>b) -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U b)
[] (c -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U (b | [] (a -> (d & !f & X(!f U e)))))
!a U ((a U ((!a U ((a U ([]!a | []a)) | []!a)) | []!a)) | []!a)
<>c -> (!c U (c & (!a U ((a U ((!a U ((a U ([]!a | []a)) | []!a)) | []!a)) | []!a))))
!(p0 U (p1 & G p2))
!(p0 U (p1 & X (p2 U p3)))
!(p0 U (p1 & (X (p2 & (F (p3 & (X (F (p4 & X (F (p5 & (X (F p6)))))))))))))
!(F (p0 & XGp1))
!(F (p0 & X (p1 & XFp2)))
!(F (p0 & X (p1 U p2)))
!(FGp0 | FGp1)
!(G (!p0 | (p1 U p2)))
!(F (p0 & (XF (p1 & XF (p2 & XF p3)))))
!(GFp0 & GFp1 & GFp2 & GFp3 & GFp4)
!((p0 U (p1 U p2)) | (p1 U (p2 U p0)) | (p2 U (p0 U p1)))
!(G (! p0 | (p1 U (G p2 | G p3))))
!(p=1Uq=1)
!(p=1U(q=1Ur=1))
!(!(p=1U(q=1Ur=1)))
!(G(F(p=1))->G(F(q=1)))
!(F(p=1)UG(q=1))
!(G(p=1)Uq=1)
!(!(F(F(p=1))<->F(p=1)))
!(!(G(F(p=1))->G(F(q=1))))
!(G(F(p=1))^G(F(q=1)))
!(p=1R(p=1|q=1))
!((X(p=1)UX(q=1))|!X(p=1Uq=1))
!((X(p=1)Uq=1)|!X(p=1U(p=1&q=1)))
!(G(p=1->F(q=1))&((X(p=1)Uq=1)|!X(p=1U(p=1&q=1))))
!(G(p=1->F(q=1))&((X(p=1)UX(q=1))|!X(p=1Uq=1)))
!(G(p=1->F(q=1)))
!(!G(p=1->X(q=1Rr=1)))
!(!(G(F(p=1))|F(G(q=1))))
!(G(F(p=1)&F(q=1)))
!(F(p=1)&F(p=0))
!(((X(q=0))&(r=0))R(X((((s=0)U(p=0))R(r=0))U((s=0)R(r=0)))))
!((G(q=1|G(F(p=1)))&G(r=1|G(F(p=0))))|G(q=1)|G(r=1))
!((G(q=1|F(G(p=1)))&G(r=1|F(G(p=0))))|G(q=1)|G(r=1))
!(!((G(q=1|G(F(p=1)))&G(r=1|G(F(p=0))))|G(q=1)|G(r=1)))
!(!((G(q=1|F(G(p=1)))&G(r=1|F(G(p=0))))|G(q=1)|G(r=1)))
!(G(q=1|X(G(p=1)))&G(r=1|X(G(p=0))))
!(G(p=1|(X(q=1)&X(q=0))))
!((p=1Uq=1)|(q=1Up=1))
!([](!a))
!(<>b -> (!a U b))
!([](c -> [](!a)))
!([]((c & !b & <>b) -> (!a U b)))
!([](c & !b -> (!a U (b | []!a))))
!(<>(a))
!(!b U ((a & !b) | []!b))
!([](!c) | <>(c & <>a))
!([](c & !b -> (!b U ((a & !b) | []!b))))
!([](c & !b -> (!b U (a & !b))))
!(<>b -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U b))))))))))
!([]((c & <>b) -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U b)))))))))))
!([](c -> ((!a & !b) U (b | ((a & !b) U (b | ((!a & !b) U (b | ((a & !b) U (b | (!a U (b | []!a)) | []a))))))))))
!([](a))
!(<>b -> (a U b))
!([](c -> [](a)))
!([]((c & !b & <>b) -> (a U b)))
!([](c & !b -> (a U (b | [] a))))
!(!a U (d | []!a))
!(<>b -> (!a U (d | b)))
!([]!c | <>(c & (!a U (d | []!a))))
!([]((c & !b & <>b) -> (!a U (d | b))))
!([](c & !b -> (!a U ((d | b) | []!a))))
!([](a -> <>d))
!(<>b -> (a -> (!b U (d & !b))) U b)
!([](c -> [](a -> <>d)))
!([]((c & !b & <>b) -> (a -> (!b U (d & !b))) U b))
!([](c & !b -> ((a -> (!b U (d & !b))) U (b | [](a -> (!b U (d & !b)))))))
!(<>a -> (!a U (d & !a & X(!a U e))))
!(<>b -> (!a U (b | (d & !a & X(!a U e)))))
!(([]!c) | (!c U (c & <>a -> (!a U (d & !a & X(!a U e))))))
!([]((c & <>b) -> (!a U (b | (d & !a & X(!a U e))))))
!([](c -> (<>a -> (!a U (b | (d & !a & X(!a U e)))))))
!((<>(d & X<>e)) -> ((!d) U a))
!(<>b -> ((!(d & (!b) & X(!b U (e & !b)))) U (b | a)))
!(([]!c) | ((!c) U (c & ((<>(d & X<>e)) -> ((!d) U a)))))
!([]((c & <>b) -> ((!(d & (!b) & X(!b U (e & !b)))) U (b | a))))
!([](c -> (!(d & (!b) & X(!b U (e & !b))) U (b | a) | [](!(d & X<>e)))))
!([] (d & X<> e -> X(<>(e & <> a))))
!(<>b -> (d & X(!b U e) -> X(!b U (e & <> a))) U b)
!([] (c -> [] (d & X<> e -> X(!e U (e & <> a)))))
!([] ((c & <>b) -> (d & X(!b U e) -> X(!b U (e & <> a))) U b))
!([] (c -> (d & X(!b U e) -> X(!b U (e & <> a))) U (b | [] (d & X(!b U e) -> X(!b U (e & <> a))))))
!([] (a -> <>(d & X<>e)))
!(<>b -> (a -> (!b U (d & !b & X(!b U e)))) U b)
!([] (c -> [] (a -> (d & X<> e))))
!([] ((c & <>b) -> (a -> (!b U (d & !b & X(!b U e)))) U b))
!([] (c -> (a -> (!b U (d & !b & X(!b U e)))) U (b | [] (a -> (d & X<> e)))))
!([] (a -> <>(d & !f & X(!f U e))))
!(<>b -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U b)
!([] (c -> [] (a -> (d & !f & X(!f U e)))))
!([] ((c & <>b) -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U b))
!([] (c -> (a -> (!b U (d & !b & !f & X((!b & !f) U e)))) U (b | [] (a -> (d & !f & X(!f U e))))))
!(!a U ((a U ((!a U ((a U ([]!a | []a)) | []!a)) | []!a)) | []!a))
!(<>c -> (!c U (c & (!a U ((a U ((!a U ((a U ([]!a | []a)) | []!a)) | []!a)) | []!a)))))
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