%   ORIGINAL: h4/Past__Temporal__Logic/SIMPLIFY_c18
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/ABS__SIMP: !t2 t1. (\x. t1) t2 = t1
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/OR__CLAUSES_c4: !t. t \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/prim__rec/LESS__REFL: !n. ~h4/prim__rec/_3C n n
% Assm: h4/prim__rec/PRE0_c0: h4/prim__rec/PRE h4/num/0 = h4/num/0
% Assm: h4/prim__rec/PRE0_c1: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm: h4/arithmetic/LESS__OR__EQ: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/Temporal__Logic/NEXT0: !P. h4/Temporal__Logic/NEXT P = (\t. P (h4/num/SUC t))
% Assm: h4/Temporal__Logic/ALWAYS0: !t0 P. h4/Temporal__Logic/ALWAYS P t0 <=> (!t. P (h4/arithmetic/_2B t t0))
% Assm: h4/Temporal__Logic/EVENTUAL0: !t0 P. h4/Temporal__Logic/EVENTUAL P t0 <=> (?t. P (h4/arithmetic/_2B t t0))
% Assm: h4/Temporal__Logic/WHEN__SIMP_c0: !b. h4/Temporal__Logic/WHEN (\t. F) b = h4/Temporal__Logic/ALWAYS (\t. ~b t)
% Assm: h4/Temporal__Logic/WHEN__SIMP_c1: !b. h4/Temporal__Logic/WHEN (\t. T) b = (\t. T)
% Assm: h4/Temporal__Logic/WHEN__SIMP_c2: !a. h4/Temporal__Logic/WHEN a (\t. F) = (\t. T)
% Assm: h4/Temporal__Logic/WHEN__SIMP_c3: !a. h4/Temporal__Logic/WHEN a (\t. T) = (\t. a t)
% Assm: h4/Temporal__Logic/WHEN__SIMP_c4: !a. h4/Temporal__Logic/WHEN a a = (\t. T)
% Assm: h4/Temporal__Logic/UNTIL__SIMP_c0: !b. h4/Temporal__Logic/UNTIL (\t. F) b = (\t. b t)
% Assm: h4/Temporal__Logic/UNTIL__SIMP_c1: !b. h4/Temporal__Logic/UNTIL (\t. T) b = (\t. T)
% Assm: h4/Temporal__Logic/UNTIL__SIMP_c2: !a. h4/Temporal__Logic/UNTIL a (\t. F) = h4/Temporal__Logic/ALWAYS a
% Assm: h4/Temporal__Logic/UNTIL__SIMP_c3: !a. h4/Temporal__Logic/UNTIL a (\t. T) = (\t. T)
% Assm: h4/Temporal__Logic/UNTIL__SIMP_c4: !a. h4/Temporal__Logic/UNTIL a a = (\t. a t)
% Assm: h4/Temporal__Logic/BEFORE__SIMP_c0: !b. h4/Temporal__Logic/BEFORE (\t. F) b = h4/Temporal__Logic/ALWAYS (\t. ~b t)
% Assm: h4/Temporal__Logic/BEFORE__SIMP_c1: !b. h4/Temporal__Logic/BEFORE (\t. T) b = (\t. ~b t)
% Assm: h4/Temporal__Logic/BEFORE__SIMP_c2: !a. h4/Temporal__Logic/BEFORE a (\t. F) = (\t. T)
% Assm: h4/Temporal__Logic/BEFORE__SIMP_c3: !a. h4/Temporal__Logic/BEFORE a (\t. T) = (\t. F)
% Assm: h4/Temporal__Logic/BEFORE__SIMP_c4: !a. h4/Temporal__Logic/BEFORE a a = h4/Temporal__Logic/ALWAYS (\t. ~a t)
% Assm: h4/Temporal__Logic/SWHEN__SIMP_c0: !b. h4/Temporal__Logic/SWHEN (\t. F) b = (\t. F)
% Assm: h4/Temporal__Logic/SWHEN__SIMP_c1: !b. h4/Temporal__Logic/SWHEN (\t. T) b = h4/Temporal__Logic/EVENTUAL b
% Assm: h4/Temporal__Logic/SWHEN__SIMP_c2: !a. h4/Temporal__Logic/SWHEN a (\t. F) = (\t. F)
% Assm: h4/Temporal__Logic/SWHEN__SIMP_c3: !a. h4/Temporal__Logic/SWHEN a (\t. T) = (\t. a t)
% Assm: h4/Temporal__Logic/SWHEN__SIMP_c4: !a. h4/Temporal__Logic/SWHEN a a = h4/Temporal__Logic/EVENTUAL a
% Assm: h4/Temporal__Logic/SUNTIL__SIMP_c0: !b. h4/Temporal__Logic/SUNTIL (\t. F) b = (\t. b t)
% Assm: h4/Temporal__Logic/SUNTIL__SIMP_c1: !b. h4/Temporal__Logic/SUNTIL (\t. T) b = h4/Temporal__Logic/EVENTUAL b
% Assm: h4/Temporal__Logic/SUNTIL__SIMP_c2: !a. h4/Temporal__Logic/SUNTIL a (\t. F) = (\t. F)
% Assm: h4/Temporal__Logic/SUNTIL__SIMP_c3: !a. h4/Temporal__Logic/SUNTIL a (\t. T) = (\t. T)
% Assm: h4/Temporal__Logic/SUNTIL__SIMP_c4: !a. h4/Temporal__Logic/SUNTIL a a = (\t. a t)
% Assm: h4/Temporal__Logic/SBEFORE__SIMP_c0: !b. h4/Temporal__Logic/SBEFORE (\t. F) b = (\t. F)
% Assm: h4/Temporal__Logic/SBEFORE__SIMP_c1: !b. h4/Temporal__Logic/SBEFORE (\t. T) b = (\t. ~b t)
% Assm: h4/Temporal__Logic/SBEFORE__SIMP_c2: !a. h4/Temporal__Logic/SBEFORE a (\t. F) = h4/Temporal__Logic/EVENTUAL a
% Assm: h4/Temporal__Logic/SBEFORE__SIMP_c3: !a. h4/Temporal__Logic/SBEFORE a (\t. T) = (\t. F)
% Assm: h4/Temporal__Logic/SBEFORE__SIMP_c4: !a. h4/Temporal__Logic/SBEFORE a a = (\t. F)
% Assm: h4/Temporal__Logic/ALWAYS__REC: !t0 P. h4/Temporal__Logic/ALWAYS P t0 <=> P t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/ALWAYS P) t0
% Assm: h4/Temporal__Logic/EVENTUAL__REC: !t0 P. h4/Temporal__Logic/EVENTUAL P t0 <=> P t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/EVENTUAL P) t0
% Assm: h4/Temporal__Logic/WHEN__REC: !t0 b a. h4/Temporal__Logic/WHEN a b t0 <=> h4/bool/COND (b t0) (a t0) (h4/Temporal__Logic/NEXT (h4/Temporal__Logic/WHEN a b) t0)
% Assm: h4/Temporal__Logic/UNTIL__REC: !t0 b a. h4/Temporal__Logic/UNTIL a b t0 <=> ~b t0 ==> a t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/UNTIL a b) t0
% Assm: h4/Temporal__Logic/BEFORE__REC: !t0 b a. h4/Temporal__Logic/BEFORE a b t0 <=> ~b t0 /\ (a t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/BEFORE a b) t0)
% Assm: h4/Temporal__Logic/SWHEN__REC: !t0 b a. h4/Temporal__Logic/SWHEN a b t0 <=> h4/bool/COND (b t0) (a t0) (h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SWHEN a b) t0)
% Assm: h4/Temporal__Logic/SUNTIL__REC: !t0 b a. h4/Temporal__Logic/SUNTIL a b t0 <=> ~b t0 ==> a t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SUNTIL a b) t0
% Assm: h4/Temporal__Logic/SBEFORE__REC: !t0 b a. h4/Temporal__Logic/SBEFORE a b t0 <=> ~b t0 /\ (a t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SBEFORE a b) t0)
% Assm: h4/Past__Temporal__Logic/InitPoint0: h4/Past__Temporal__Logic/InitPoint = (\t. t = h4/num/0)
% Assm: h4/Past__Temporal__Logic/PSNEXT0: !t0 a. h4/Past__Temporal__Logic/PSNEXT a t0 <=> h4/prim__rec/_3C h4/num/0 t0 /\ a (h4/prim__rec/PRE t0)
% Assm: h4/Past__Temporal__Logic/PNEXT0: !t0 a. h4/Past__Temporal__Logic/PNEXT a t0 <=> t0 = h4/num/0 \/ a (h4/prim__rec/PRE t0)
% Assm: h4/Past__Temporal__Logic/PALWAYS0: !t0 a. h4/Past__Temporal__Logic/PALWAYS a t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> a t)
% Assm: h4/Past__Temporal__Logic/PEVENTUAL0: !t0 a. h4/Past__Temporal__Logic/PEVENTUAL a t0 <=> (?t. h4/arithmetic/_3C_3D t t0 /\ a t)
% Assm: h4/Past__Temporal__Logic/PSWHEN0: !t0 b a. h4/Past__Temporal__Logic/PSWHEN a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ a delta /\ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~b t))
% Assm: h4/Past__Temporal__Logic/PSUNTIL0: !t0 b a. h4/Past__Temporal__Logic/PSUNTIL a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> a t /\ ~b t))
% Assm: h4/Past__Temporal__Logic/PSBEFORE0: !t0 b a. h4/Past__Temporal__Logic/PSBEFORE a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ a delta /\ (!t. h4/arithmetic/_3C_3D delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~b t))
% Assm: h4/Past__Temporal__Logic/PWHEN0: !t0 b a. h4/Past__Temporal__Logic/PWHEN a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> ~b t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ a delta /\ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~b t))
% Assm: h4/Past__Temporal__Logic/PUNTIL0: !t0 b a. h4/Past__Temporal__Logic/PUNTIL a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> a t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> a t /\ ~b t))
% Assm: h4/Past__Temporal__Logic/PBEFORE0: !t0 b a. h4/Past__Temporal__Logic/PBEFORE a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> ~b t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ a delta /\ (!t. h4/arithmetic/_3C_3D delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~b t))
% Goal: !a. h4/Temporal__Logic/SWHEN a (\t. F) = (\t. F)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_ABSu_u_SIMP]: !t2 t1. t1 = t1
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c4]: !t. t \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_primu_u_recs_LESSu_u_REFL]: !n. ~h4/prim__rec/_3C n n
% Assm [h4s_primu_u_recs_PRE0u_c0]: h4/prim__rec/PRE h4/num/0 = h4/num/0
% Assm [h4s_primu_u_recs_PRE0u_c1]: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm [h4s_arithmetics_LESSu_u_ORu_u_EQ]: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_Temporalu_u_Logics_NEXT0]: !P x. h4/Temporal__Logic/NEXT P x <=> happ P (h4/num/SUC x)
% Assm [h4s_Temporalu_u_Logics_ALWAYS0]: !t0 P. happ (h4/Temporal__Logic/ALWAYS P) t0 <=> (!t. happ P (h4/arithmetic/_2B t t0))
% Assm [h4s_Temporalu_u_Logics_EVENTUAL0]: !t0 P. happ (h4/Temporal__Logic/EVENTUAL P) t0 <=> (?t. happ P (h4/arithmetic/_2B t t0))
% Assm [h4s_Temporalu_u_Logics_WHENu_u_SIMPu_c0]: !_1. (!b t. happ (happ _1 b) t <=> ~happ b t) ==> (!_0. (!t. happ _0 t <=> F) ==> (!b. h4/Temporal__Logic/WHEN _0 b = h4/Temporal__Logic/ALWAYS (happ _1 b)))
% Assm [h4s_Temporalu_u_Logics_WHENu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b x. happ (h4/Temporal__Logic/WHEN _0 b) x <=> T)
% Assm [h4s_Temporalu_u_Logics_WHENu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a x. happ (h4/Temporal__Logic/WHEN a _0) x <=> T)
% Assm [h4s_Temporalu_u_Logics_WHENu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/WHEN a _0) x <=> happ a x)
% Assm [h4s_Temporalu_u_Logics_WHENu_u_SIMPu_c4]: !a x. happ (h4/Temporal__Logic/WHEN a a) x <=> T
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c0]: !_0. (!t. happ _0 t <=> F) ==> (!b x. happ (h4/Temporal__Logic/UNTIL _0 b) x <=> happ b x)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b x. happ (h4/Temporal__Logic/UNTIL _0 b) x <=> T)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a. h4/Temporal__Logic/UNTIL a _0 = h4/Temporal__Logic/ALWAYS a)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/UNTIL a _0) x <=> T)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c4]: !a x. happ (h4/Temporal__Logic/UNTIL a a) x <=> happ a x
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c0]: !_1. (!b t. happ (happ _1 b) t <=> ~happ b t) ==> (!_0. (!t. happ _0 t <=> F) ==> (!b. h4/Temporal__Logic/BEFORE _0 b = h4/Temporal__Logic/ALWAYS (happ _1 b)))
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b x. happ (h4/Temporal__Logic/BEFORE _0 b) x <=> ~happ b x)
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a x. happ (h4/Temporal__Logic/BEFORE a _0) x <=> T)
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/BEFORE a _0) x <=> F)
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c4]: !_0. (!a t. happ (happ _0 a) t <=> ~happ a t) ==> (!a. h4/Temporal__Logic/BEFORE a a = h4/Temporal__Logic/ALWAYS (happ _0 a))
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c0]: !_0. (!t. happ _0 t <=> F) ==> (!b x. happ (h4/Temporal__Logic/SWHEN _0 b) x <=> F)
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b. h4/Temporal__Logic/SWHEN _0 b = h4/Temporal__Logic/EVENTUAL b)
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a x. happ (h4/Temporal__Logic/SWHEN a _0) x <=> F)
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/SWHEN a _0) x <=> happ a x)
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c4]: !a. h4/Temporal__Logic/SWHEN a a = h4/Temporal__Logic/EVENTUAL a
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c0]: !_0. (!t. happ _0 t <=> F) ==> (!b x. happ (h4/Temporal__Logic/SUNTIL _0 b) x <=> happ b x)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b. h4/Temporal__Logic/SUNTIL _0 b = h4/Temporal__Logic/EVENTUAL b)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a x. happ (h4/Temporal__Logic/SUNTIL a _0) x <=> F)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/SUNTIL a _0) x <=> T)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c4]: !a x. happ (h4/Temporal__Logic/SUNTIL a a) x <=> happ a x
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c0]: !_0. (!t. happ _0 t <=> F) ==> (!b x. happ (h4/Temporal__Logic/SBEFORE _0 b) x <=> F)
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c1]: !_0. (!t. happ _0 t <=> T) ==> (!b x. happ (h4/Temporal__Logic/SBEFORE _0 b) x <=> ~happ b x)
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c2]: !_0. (!t. happ _0 t <=> F) ==> (!a. h4/Temporal__Logic/SBEFORE a _0 = h4/Temporal__Logic/EVENTUAL a)
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c3]: !_0. (!t. happ _0 t <=> T) ==> (!a x. happ (h4/Temporal__Logic/SBEFORE a _0) x <=> F)
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c4]: !a x. happ (h4/Temporal__Logic/SBEFORE a a) x <=> F
% Assm [h4s_Temporalu_u_Logics_ALWAYSu_u_REC]: !t0 P. happ (h4/Temporal__Logic/ALWAYS P) t0 <=> happ P t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/ALWAYS P) t0
% Assm [h4s_Temporalu_u_Logics_EVENTUALu_u_REC]: !t0 P. happ (h4/Temporal__Logic/EVENTUAL P) t0 <=> happ P t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/EVENTUAL P) t0
% Assm [h4s_Temporalu_u_Logics_WHENu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/WHEN a b) t0 <=> h4/bool/COND (happ b t0) (happ a t0) (h4/Temporal__Logic/NEXT (h4/Temporal__Logic/WHEN a b) t0)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/UNTIL a b) t0 <=> ~happ b t0 ==> happ a t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/UNTIL a b) t0
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/BEFORE a b) t0 <=> ~happ b t0 /\ (happ a t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/BEFORE a b) t0)
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/SWHEN a b) t0 <=> h4/bool/COND (happ b t0) (happ a t0) (h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SWHEN a b) t0)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/SUNTIL a b) t0 <=> ~happ b t0 ==> happ a t0 /\ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SUNTIL a b) t0
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_REC]: !t0 b a. happ (h4/Temporal__Logic/SBEFORE a b) t0 <=> ~happ b t0 /\ (happ a t0 \/ h4/Temporal__Logic/NEXT (h4/Temporal__Logic/SBEFORE a b) t0)
% Assm [h4s_Pastu_u_Temporalu_u_Logics_InitPoint0]: !x. h4/Past__Temporal__Logic/InitPoint x <=> x = h4/num/0
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PSNEXT0]: !t0 a. h4/Past__Temporal__Logic/PSNEXT a t0 <=> h4/prim__rec/_3C h4/num/0 t0 /\ happ a (h4/prim__rec/PRE t0)
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PNEXT0]: !t0 a. h4/Past__Temporal__Logic/PNEXT a t0 <=> t0 = h4/num/0 \/ happ a (h4/prim__rec/PRE t0)
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PALWAYS0]: !t0 a. h4/Past__Temporal__Logic/PALWAYS a t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> happ a t)
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PEVENTUAL0]: !t0 a. h4/Past__Temporal__Logic/PEVENTUAL a t0 <=> (?t. h4/arithmetic/_3C_3D t t0 /\ happ a t)
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PSWHEN0]: !t0 b a. h4/Past__Temporal__Logic/PSWHEN a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ a delta /\ happ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~happ b t))
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PSUNTIL0]: !t0 b a. h4/Past__Temporal__Logic/PSUNTIL a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> happ a t /\ ~happ b t))
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PSBEFORE0]: !t0 b a. h4/Past__Temporal__Logic/PSBEFORE a b t0 <=> (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ a delta /\ (!t. h4/arithmetic/_3C_3D delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~happ b t))
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PWHEN0]: !t0 b a. h4/Past__Temporal__Logic/PWHEN a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> ~happ b t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ a delta /\ happ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~happ b t))
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PUNTIL0]: !t0 b a. h4/Past__Temporal__Logic/PUNTIL a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> happ a t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ b delta /\ (!t. h4/prim__rec/_3C delta t /\ h4/arithmetic/_3C_3D t t0 ==> happ a t /\ ~happ b t))
% Assm [h4s_Pastu_u_Temporalu_u_Logics_PBEFORE0]: !t0 b a. h4/Past__Temporal__Logic/PBEFORE a b t0 <=> (!t. h4/arithmetic/_3C_3D t t0 ==> ~happ b t) \/ (?delta. h4/arithmetic/_3C_3D delta t0 /\ happ a delta /\ (!t. h4/arithmetic/_3C_3D delta t /\ h4/arithmetic/_3C_3D t t0 ==> ~happ b t))
% Goal: !_0. (!t. happ _0 t <=> F) ==> (!a x. happ (h4/Temporal__Logic/SWHEN a _0) x <=> F)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q325014,TV_Q325010]: ![V_f, V_g]: (![V_x]: s(TV_Q325010,happ(s(t_fun(TV_Q325014,TV_Q325010),V_f),s(TV_Q325014,V_x))) = s(TV_Q325010,happ(s(t_fun(TV_Q325014,TV_Q325010),V_g),s(TV_Q325014,V_x))) => s(t_fun(TV_Q325014,TV_Q325010),V_f) = s(t_fun(TV_Q325014,TV_Q325010),V_g))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ABSu_u_SIMP, axiom, ![TV_u_27b,TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,V_t1) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t0))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t0))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t0) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_primu_u_recs_LESSu_u_REFL, axiom, ![V_n]: ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_primu_u_recs_PRE0u_c0, axiom, s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_primu_u_recs_PRE0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_ORu_u_EQ, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) | s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_Temporalu_u_Logics_NEXT0, axiom, ![V_P, V_x]: s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_x)))))).
fof(ah4s_Temporalu_u_Logics_ALWAYS0, axiom, ![V_t0, V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0)))) <=> ![V_t]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_EVENTUAL0, axiom, ![V_t0, V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0)))) <=> ?[V_t]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_SIMPu_c0, axiom, ![V_uu_1]: (![V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_b)))))))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_x))))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_SIMPu_c4, axiom, ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0)).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c0, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_x))))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),V_a))))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_SIMPu_c4, axiom, ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_x)))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c0, axiom, ![V_uu_1]: (![V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_b)))))))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b, V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_x)))))))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_SIMPu_c4, axiom, ![V_uu_0]: (![V_a, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))))) => ![V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))))))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c0, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_b))))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_x))))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_SIMPu_c4, axiom, ![V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_a)))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c0, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_x))))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_b))))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,t0))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_SIMPu_c4, axiom, ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_x)))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c0, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_b, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c1, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_b, V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_x)))))))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c2, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_a))))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c3, axiom, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,t0) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_SIMPu_c4, axiom, ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_x))) = s(t_bool,f)).
fof(ah4s_Temporalu_u_Logics_ALWAYSu_u_REC, axiom, ![V_t0, V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_t0)))) & p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0))))))).
fof(ah4s_Temporalu_u_Logics_EVENTUALu_u_REC, axiom, ![V_t0, V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_t0)))) | p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_P))),s(t_h4s_nums_num,V_t0))))))).
fof(ah4s_Temporalu_u_Logics_WHENu_u_REC, axiom, ![V_t0, V_b, V_a]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0))) = s(t_bool,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0))),s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_REC, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) & p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_REC, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) | p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_REC, axiom, ![V_t0, V_b, V_a]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0))) = s(t_bool,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0))),s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_REC, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) & p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_REC, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) | p(s(t_bool,h4s_temporalu_u_logics_next(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_InitPoint0, axiom, ![V_x]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_initpoint(s(t_h4s_nums_num,V_x)))) <=> s(t_h4s_nums_num,V_x) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PSNEXT0, axiom, ![V_t0, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_psnext(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_t0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_t0))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PNEXT0, axiom, ![V_t0, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pnext(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) <=> (s(t_h4s_nums_num,V_t0) = s(t_h4s_nums_num,h4s_nums_0) | p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_t0))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PALWAYS0, axiom, ![V_t0, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_palways(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) <=> ![V_t]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PEVENTUAL0, axiom, ![V_t0, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_peventual(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) <=> ?[V_t]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PSWHEN0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pswhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_delta)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t))))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PSUNTIL0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_psuntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) & ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t))))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PSBEFORE0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_psbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PWHEN0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pwhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> (![V_t]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) | ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_delta)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PUNTIL0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_puntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> (![V_t]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t))))) | ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) & ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))))))))).
fof(ah4s_Pastu_u_Temporalu_u_Logics_PBEFORE0, axiom, ![V_t0, V_b, V_a]: (p(s(t_bool,h4s_pastu_u_temporalu_u_logics_pbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))) <=> (![V_t]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0)))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) | ?[V_delta]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t0)))) & (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_delta)))) & ![V_t]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_delta),s(t_h4s_nums_num,V_t)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_t),s(t_h4s_nums_num,V_t0))))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t))))))))))).
fof(ch4s_Pastu_u_Temporalu_u_Logics_SIMPLIFYu_c18, conjecture, ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_uu_0))),s(t_h4s_nums_num,V_x))) = s(t_bool,f))).
