%   ORIGINAL: h4/enumeral/OU__ASSOC
% 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/enumeral/OU0: !u t cmp. h4/enumeral/OU cmp t u = h4/pred__set/UNION (h4/pred__set/GSPEC (\x. h4/pair/_2C x (h4/bool/IN x t /\ (!z. h4/bool/IN z u ==> h4/toto/apto cmp x z = h4/toto/LESS)))) u
% Assm: h4/enumeral/LESS__ALL__OU: !x v u cmp. h4/enumeral/LESS__ALL cmp x (h4/enumeral/OU cmp u v) <=> h4/enumeral/LESS__ALL cmp x u /\ h4/enumeral/LESS__ALL cmp x v
% Assm: h4/enumeral/EMPTY__OU: !sl cmp. h4/enumeral/OU cmp h4/pred__set/EMPTY sl = sl
% Assm: h4/enumeral/OU__EMPTY: !t cmp. h4/enumeral/OU cmp t h4/pred__set/EMPTY = t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/pred__set/UNION__EMPTY_c0: !s. h4/pred__set/UNION h4/pred__set/EMPTY s = s
% Assm: h4/pred__set/GSPEC__F: h4/pred__set/GSPEC (\x. h4/pair/_2C x F) = h4/pred__set/EMPTY
% Assm: h4/pred__set/UNION__EMPTY_c1: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm: h4/pred__set/GSPEC__ID: !y. h4/pred__set/GSPEC (\x. h4/pair/_2C x (h4/bool/IN x y)) = y
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/toto/toto__equal__sym: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> h4/toto/apto c y x = h4/toto/EQUAL
% Assm: h4/enumeral/LESS__ALL0: !x s cmp. h4/enumeral/LESS__ALL cmp x s <=> (!y. h4/bool/IN y s ==> h4/toto/apto cmp x y = h4/toto/LESS)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/pair/PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/pred__set/GSPECIFICATION: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = f x)
% Assm: h4/toto/toto__trans__less_c0: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/pred__set/IN__UNION: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/toto/toto__refl: !x c. h4/toto/apto c x x = h4/toto/EQUAL
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% 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/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/pred__set/SUBSET__DEF: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/toto/toto__trans__less_c1: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/cpn__nchotomy: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/toto/toto__trans__less_c3: !z y x c. h4/toto/apto c y x = h4/toto/GREATER /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/toto/toto__trans__less_c4: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/toto/all__cpn__distinct_c3: ~(h4/toto/EQUAL = h4/toto/LESS)
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/sat/dc__cond: !s r q p. (p <=> h4/bool/COND q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~p)
% Assm: h4/enumeral/UO0: !t s cmp. h4/enumeral/UO cmp s t = h4/pred__set/UNION s (h4/pred__set/GSPEC (\y. h4/pair/_2C y (h4/bool/IN y t /\ (!z. h4/bool/IN z s ==> h4/toto/apto cmp z y = h4/toto/LESS))))
% Assm: h4/enumeral/LESS__UO__LEM: !y x s cmp. (!z. h4/bool/IN z (h4/enumeral/UO cmp (h4/pred__set/INSERT x h4/pred__set/EMPTY) s) ==> h4/toto/apto cmp y z = h4/toto/LESS) <=> h4/toto/apto cmp y x = h4/toto/LESS
% Assm: h4/enumeral/OWL0: !s l cmp. h4/enumeral/OWL cmp s l <=> s = h4/list/LIST__TO__SET l /\ h4/enumeral/OL cmp l
% Assm: h4/enumeral/smerge__tupled__primitive: h4/enumeral/smerge__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/EQUAL ==> R (h4/pair/_2C cmp (h4/pair/_2C l m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m)))) /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/GREATER ==> R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) m)) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m)))) /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/LESS ==> R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m)))))) (\smerge__tupled a. h4/pair/pair__CASE a (\cmp v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (\y m. h4/combin/I (h4/list/CONS y m))) (\x l. h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS x l)) (\y_27 m_27. h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp x y_27) (h4/list/CONS x (smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y_27 m_27))))) (h4/list/CONS x (smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m_27)))) (h4/list/CONS y_27 (smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) m_27))))))))))
% Assm: h4/toto/aplextoto: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm: h4/toto/toto__equal__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/pred__set/IN__SING: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm: h4/bool/UNWIND__FORALL__THM2: !v f. (!x. x = v ==> f x) <=> f v
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/iSUB__THM_c8: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iDUB__removal_c0: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% 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/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c8: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c20: !n. h4/prim__rec/_3C n h4/num/0 <=> F
% 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/arithmetic/SUB__LEFT__EQ: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ 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/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% 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/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% 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/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 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: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/arithmetic/SUB__LEFT__LESS: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% 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/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/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/relation/WeakLinearOrder0: !R. h4/relation/WeakLinearOrder R <=> h4/relation/WeakOrder R /\ h4/relation/trichotomous R
% Assm: h4/relation/StrongLinearOrder0: !R. h4/relation/StrongLinearOrder R <=> h4/relation/StrongOrder R /\ h4/relation/trichotomous R
% Assm: h4/relation/STRORD0: !b a R. h4/relation/STRORD R a b <=> R a b /\ ~(a = b)
% Goal: !cmp c b a. h4/enumeral/OU cmp a (h4/enumeral/OU cmp b c) = h4/enumeral/OU cmp (h4/enumeral/OU cmp a b) c
%   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_enumerals_OU0]: !_0. (!t u cmp x. ?v. (v <=> h4/bool/IN x t /\ (!z. h4/bool/IN z u ==> h4/toto/apto cmp x z = h4/toto/LESS)) /\ happ (happ (happ (happ _0 t) u) cmp) x = h4/pair/_2C x v) ==> (!u t cmp. h4/enumeral/OU cmp t u = h4/pred__set/UNION (h4/pred__set/GSPEC (happ (happ (happ _0 t) u) cmp)) u)
% Assm [h4s_enumerals_LESSu_u_ALLu_u_OU]: !x v u cmp. h4/enumeral/LESS__ALL cmp x (h4/enumeral/OU cmp u v) <=> h4/enumeral/LESS__ALL cmp x u /\ h4/enumeral/LESS__ALL cmp x v
% Assm [h4s_enumerals_EMPTYu_u_OU]: !sl cmp. h4/enumeral/OU cmp h4/pred__set/EMPTY sl = sl
% Assm [h4s_enumerals_OUu_u_EMPTY]: !t cmp. h4/enumeral/OU cmp t h4/pred__set/EMPTY = t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> 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_predu_u_sets_UNIONu_u_EMPTYu_c0]: !s. h4/pred__set/UNION h4/pred__set/EMPTY s = s
% Assm [h4s_predu_u_sets_GSPECu_u_F]: !_0. (!x. happ _0 x = h4/pair/_2C x F) ==> h4/pred__set/GSPEC _0 = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_UNIONu_u_EMPTYu_c1]: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm [h4s_predu_u_sets_GSPECu_u_ID]: !_0. (!y x. happ (happ _0 y) x = h4/pair/_2C x (h4/bool/IN x y)) ==> (!y. h4/pred__set/GSPEC (happ _0 y) = y)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_totos_totou_u_equalu_u_sym]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> h4/toto/apto c y x = h4/toto/EQUAL
% Assm [h4s_enumerals_LESSu_u_ALL0]: !x s cmp. h4/enumeral/LESS__ALL cmp x s <=> (!y. h4/bool/IN y s ==> h4/toto/apto cmp x y = h4/toto/LESS)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_pairs_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_predu_u_sets_GSPECIFICATION]: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = happ f x)
% Assm [h4s_totos_totou_u_transu_u_lessu_c0]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_predu_u_sets_INu_u_UNION]: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_totos_totou_u_refl]: !x c. h4/toto/apto c x x = h4/toto/EQUAL
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% 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_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_predu_u_sets_SUBSETu_u_DEF]: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_totos_totou_u_transu_u_lessu_c1]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_totos_cpnu_u_nchotomy]: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_totos_totou_u_transu_u_lessu_c3]: !z y x c. h4/toto/apto c y x = h4/toto/GREATER /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_totos_totou_u_transu_u_lessu_c4]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c3]: ~(h4/toto/EQUAL = h4/toto/LESS)
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_sats_dcu_u_cond]: !s r q p. (p <=> h4/bool/COND q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~p)
% Assm [h4s_enumerals_UO0]: !_0. (!t s cmp y. ?v. (v <=> h4/bool/IN y t /\ (!z. h4/bool/IN z s ==> h4/toto/apto cmp z y = h4/toto/LESS)) /\ happ (happ (happ (happ _0 t) s) cmp) y = h4/pair/_2C y v) ==> (!t s cmp. h4/enumeral/UO cmp s t = h4/pred__set/UNION s (h4/pred__set/GSPEC (happ (happ (happ _0 t) s) cmp)))
% Assm [h4s_enumerals_LESSu_u_UOu_u_LEM]: !y x s cmp. (!z. h4/bool/IN z (h4/enumeral/UO cmp (h4/pred__set/INSERT x h4/pred__set/EMPTY) s) ==> h4/toto/apto cmp y z = h4/toto/LESS) <=> h4/toto/apto cmp y x = h4/toto/LESS
% Assm [h4s_enumerals_OWL0]: !s l cmp. h4/enumeral/OWL cmp s l <=> s = h4/list/LIST__TO__SET l /\ h4/enumeral/OL cmp l
% Assm [h4s_enumerals_smergeu_u_tupledu_u_primitive]: !_12. (!y_27 smerge__tupled cmp x l m_27. happ (happ (happ (happ (happ (happ _12 y_27) smerge__tupled) cmp) x) l) m_27 = h4/combin/I (h4/toto/cpn__CASE (h4/toto/apto cmp x y_27) (h4/list/CONS x (happ smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y_27 m_27))))) (h4/list/CONS x (happ smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C l m_27)))) (h4/list/CONS y_27 (happ smerge__tupled (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) m_27)))))) ==> (!_11. (!smerge__tupled cmp x l y_27. happ (happ (happ (happ (happ _11 smerge__tupled) cmp) x) l) y_27 = happ (happ (happ (happ (happ _12 y_27) smerge__tupled) cmp) x) l) ==> (!_10. (!v3 smerge__tupled cmp x l. happ (happ (happ (happ (happ _10 v3) smerge__tupled) cmp) x) l = h4/list/list__CASE v3 (h4/combin/I (h4/list/CONS x l)) (happ (happ (happ (happ _11 smerge__tupled) cmp) x) l)) ==> (!_9. (!v3 smerge__tupled cmp x. happ (happ (happ (happ _9 v3) smerge__tupled) cmp) x = happ (happ (happ (happ _10 v3) smerge__tupled) cmp) x) ==> (!_8. (!y m. happ (happ _8 y) m = h4/combin/I (h4/list/CONS y m)) ==> (!_7. (!y. happ _7 y = happ _8 y) ==> (!_6. (!v2 smerge__tupled cmp v3. happ (happ (happ (happ _6 v2) smerge__tupled) cmp) v3 = h4/list/list__CASE v2 (h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) _7) (happ (happ (happ _9 v3) smerge__tupled) cmp)) ==> (!_5. (!smerge__tupled cmp v2. happ (happ (happ _5 smerge__tupled) cmp) v2 = happ (happ (happ _6 v2) smerge__tupled) cmp) ==> (!_4. (!smerge__tupled cmp v1. happ (happ (happ _4 smerge__tupled) cmp) v1 = h4/pair/pair__CASE v1 (happ (happ _5 smerge__tupled) cmp)) ==> (!_3. (!smerge__tupled cmp. happ (happ _3 smerge__tupled) cmp = happ (happ _4 smerge__tupled) cmp) ==> (!_2. (!smerge__tupled a. happ (happ _2 smerge__tupled) a = h4/pair/pair__CASE a (happ _3 smerge__tupled)) ==> (!_1. (!smerge__tupled. happ _1 smerge__tupled = happ _2 smerge__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/EQUAL ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m)))) /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/GREATER ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) m))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m)))) /\ (!m l y x cmp. h4/toto/apto cmp x y = h4/toto/LESS ==> happ (happ R (h4/pair/_2C cmp (h4/pair/_2C l (h4/list/CONS y m)))) (h4/pair/_2C cmp (h4/pair/_2C (h4/list/CONS x l) (h4/list/CONS y m))))) ==> h4/enumeral/smerge__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_totos_aplextoto]: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm [h4s_totos_totou_u_equalu_u_eq]: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_predu_u_sets_INu_u_SING]: !y x. h4/bool/IN x (h4/pred__set/INSERT y h4/pred__set/EMPTY) <=> x = y
% Assm [h4s_bools_UNWINDu_u_FORALLu_u_THM2]: !v f. (!x. x = v ==> happ f x) <=> happ f v
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_iSUBu_u_THMu_c8]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iDUBu_u_removalu_c0]: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% 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_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% 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_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% 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_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c8]: !n m. h4/arithmetic/_2D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m)
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c20]: !n. h4/prim__rec/_3C n h4/num/0 <=> F
% 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_arithmetics_SUBu_u_LEFTu_u_EQ]: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ 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_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% 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_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_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_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 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_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESS]: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% 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_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_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_relations_WeakLinearOrder0]: !R. h4/relation/WeakLinearOrder R <=> h4/relation/WeakOrder R /\ h4/relation/trichotomous R
% Assm [h4s_relations_StrongLinearOrder0]: !R. h4/relation/StrongLinearOrder R <=> h4/relation/StrongOrder R /\ h4/relation/trichotomous R
% Assm [h4s_relations_STRORD0]: !b a R. h4/relation/STRORD R a b <=> happ (happ R a) b /\ ~(a = b)
% Goal: !cmp c b a. h4/enumeral/OU cmp a (h4/enumeral/OU cmp b c) = h4/enumeral/OU cmp (h4/enumeral/OU cmp a b) c
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1429112,TV_Q1429108]: ![V_f, V_g]: (![V_x]: s(TV_Q1429108,happ(s(t_fun(TV_Q1429112,TV_Q1429108),V_f),s(TV_Q1429112,V_x))) = s(TV_Q1429108,happ(s(t_fun(TV_Q1429112,TV_Q1429108),V_g),s(TV_Q1429112,V_x))) => s(t_fun(TV_Q1429112,TV_Q1429108),V_f) = s(t_fun(TV_Q1429112,TV_Q1429108),V_g))).
fof(ah4s_enumerals_OU0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_t, V_u, V_cmp, V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t)))) & ![V_z]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_z),s(t_fun(TV_u_27a,t_bool),V_u)))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)))) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_u))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,V_v)))) => ![V_u, V_t, V_cmp]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_u))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_u))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))),s(t_fun(TV_u_27a,t_bool),V_u))))).
fof(ah4s_enumerals_LESSu_u_ALLu_u_OU, axiom, ![TV_u_27a]: ![V_x, V_v, V_u, V_cmp]: (p(s(t_bool,h4s_enumerals_lessu_u_all(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_u),s(t_fun(TV_u_27a,t_bool),V_v)))))) <=> (p(s(t_bool,h4s_enumerals_lessu_u_all(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_u)))) & p(s(t_bool,h4s_enumerals_lessu_u_all(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_v))))))).
fof(ah4s_enumerals_EMPTYu_u_OU, axiom, ![TV_u_27a]: ![V_sl, V_cmp]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(t_fun(TV_u_27a,t_bool),V_sl))) = s(t_fun(TV_u_27a,t_bool),V_sl)).
fof(ah4s_enumerals_OUu_u_EMPTY, axiom, ![TV_u_27a]: ![V_t, V_cmp]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27a,t_bool),V_t)).
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_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,t)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
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,t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> 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_predu_u_sets_UNIONu_u_EMPTYu_c0, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_predu_u_sets_GSPECu_u_F, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_uu_0),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,f))) => s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_uu_0))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))).
fof(ah4s_predu_u_sets_UNIONu_u_EMPTYu_c1, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_predu_u_sets_GSPECu_u_ID, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_y, V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_y))),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_y))))) => ![V_y]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_y))))) = s(t_fun(TV_u_27a,t_bool),V_y))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_totos_totou_u_equalu_u_sym, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_enumerals_LESSu_u_ALL0, axiom, ![TV_u_27a]: ![V_x, V_s, V_cmp]: (p(s(t_bool,h4s_enumerals_lessu_u_all(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) <=> ![V_y]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> 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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_pairs_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
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_predu_u_sets_GSPECIFICATION, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_v),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f)))))) <=> ?[V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_v),s(t_bool,t))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f),s(TV_u_27b,V_x))))).
fof(ah4s_totos_totou_u_transu_u_lessu_c0, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_predu_u_sets_INu_u_UNION, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
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_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_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_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_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_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_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
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_totos_totou_u_refl, axiom, ![TV_u_27a]: ![V_x, V_c]: s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_equal)).
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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
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_sats_dcu_u_imp, 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_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_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
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_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_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_predu_u_sets_SUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_totos_totou_u_transu_u_lessu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_z),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_cpnu_u_nchotomy, axiom, ![V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_less) | (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_equal) | s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_greater)))).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) | ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_totos_totou_u_transu_u_lessu_c3, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_greater) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
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_totos_totou_u_transu_u_lessu_c4, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_equal)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
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_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_totos_allu_u_cpnu_u_distinctu_c3, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_bools_LEFTu_u_ORu_u_OVERu_u_AND, 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_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_x)))))).
fof(ah4s_sats_dcu_u_cond, axiom, ![V_s, V_r, V_q, V_p]: (s(t_bool,V_p) = s(t_bool,h4s_bools_cond(s(t_bool,V_q),s(t_bool,V_r),s(t_bool,V_s))) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_s))))) & ((p(s(t_bool,V_p)) | (~ (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_s))))) & ((~ (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_s)) | ~ (p(s(t_bool,V_p))))))))))).
fof(ah4s_enumerals_UO0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_t, V_s, V_cmp, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_t)))) & ![V_z]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_z),s(t_fun(TV_u_27a,t_bool),V_s)))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_z),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less)))) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_y),s(t_bool,V_v)))) => ![V_t, V_s, V_cmp]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_uo(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))))))).
fof(ah4s_enumerals_LESSu_u_UOu_u_LEM, axiom, ![TV_u_27a]: ![V_y, V_x, V_s, V_cmp]: (![V_z]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_z),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_uo(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))),s(t_fun(TV_u_27a,t_bool),V_s)))))) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_enumerals_OWL0, axiom, ![TV_u_27a]: ![V_s, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_owl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_s),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))) & p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_enumerals_smergeu_u_tupledu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_12]: (![V_yu_27, V_smergeu_u_tupled, V_cmp, V_x, V_l, V_mu_27]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))))),V_uu_12),s(TV_u_27a,V_yu_27))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_mu_27))) = s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_yu_27))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_yu_27),s(t_h4s_lists_list(TV_u_27a),V_mu_27))))))))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_mu_27))))))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_yu_27),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_mu_27))))))))))))) => ![V_uu_11]: (![V_smergeu_u_tupled, V_cmp, V_x, V_l, V_yu_27]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(TV_u_27a,V_yu_27))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))))),V_uu_12),s(TV_u_27a,V_yu_27))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))) => ![V_uu_10]: (![V_v3, V_smergeu_u_tupled, V_cmp, V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v3),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) => ![V_uu_9]: (![V_v3, V_smergeu_u_tupled, V_cmp, V_x]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_x))) => ![V_uu_8]: (![V_y, V_m]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_uu_8),s(TV_u_27a,V_y))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))) => ![V_uu_7]: (![V_y]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_uu_7),s(TV_u_27a,V_y))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_uu_8),s(TV_u_27a,V_y))) => ![V_uu_6]: (![V_v2, V_smergeu_u_tupled, V_cmp, V_v3]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_h4s_lists_list(TV_u_27a),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_v3))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v2),s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_v3),s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_uu_7))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27a),V_v3))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_5]: (![V_smergeu_u_tupled, V_cmp, V_v2]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_lists_list(TV_u_27a),V_v2))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),V_uu_6),s(t_h4s_lists_list(TV_u_27a),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_4]: (![V_smergeu_u_tupled, V_cmp, V_v1]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),V_v1))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),V_v1),s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))))) => ![V_uu_3]: (![V_smergeu_u_tupled, V_cmp]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_totos_toto(TV_u_27a),V_cmp))) => ![V_uu_2]: (![V_smergeu_u_tupled, V_a]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_a))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),V_a),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))))) => ![V_uu_1]: (![V_smergeu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),V_smergeu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R)))) & (![V_m, V_l, V_y, V_x, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & (![V_m, V_l, V_y, V_x, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))) & ![V_m, V_l, V_y, V_x, V_cmp]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))),s(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_y),s(t_h4s_lists_list(TV_u_27a),V_m))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),h4s_enumerals_smergeu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_totos_toto(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_h4s_lists_list(TV_u_27a))),V_uu_1))))))))))))))))).
fof(ah4s_totos_aplextoto, axiom, ![TV_u_27a,TV_u_27b]: ![V_y2, V_y1, V_x2, V_x1, V_v, V_c]: s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_lextoto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(t_h4s_totos_toto(TV_u_27b),V_v))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(TV_u_27b,V_x2))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_y1),s(TV_u_27b,V_y2))))) = s(t_h4s_totos_cpn,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x1),s(TV_u_27a,V_y1))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27b),V_v),s(TV_u_27b,V_x2),s(TV_u_27b,V_y2))),s(t_h4s_totos_cpn,h4s_totos_greater)))).
fof(ah4s_totos_totou_u_equalu_u_eq, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
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_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => 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,t))) <=> p(s(t_bool,t)))).
fof(ah4s_predu_u_sets_INu_u_SING, axiom, ![TV_u_27a]: ![V_y, V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_bools_UNWINDu_u_FORALLu_u_THM2, axiom, ![TV_u_27a]: ![V_v, V_f]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_v) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_v)))))).
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_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_iSUBu_u_THMu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit2(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_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iDUBu_u_removalu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),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_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,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))))))).
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_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(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_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
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_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
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_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
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_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_distribu_c17, axiom, ![V_n]: (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_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_numerals_numeralu_u_distribu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
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_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c20, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,f)).
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_arithmetics_SUBu_u_LEFTu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(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,V_m),s(t_h4s_nums_num,V_p))) = 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,h4s_nums_0)))) & 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_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_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_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_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_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_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_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_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_LESS, axiom, ![V_p, 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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_primu_u_recs_u_3c(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_h4s_nums_num,V_n)))).
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_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_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_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_relations_WeakLinearOrder0, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_weaklinearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_weakorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & p(s(t_bool,h4s_relations_trichotomous(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))))).
fof(ah4s_relations_StrongLinearOrder0, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_stronglinearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_strongorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & p(s(t_bool,h4s_relations_trichotomous(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))))).
fof(ah4s_relations_STRORD0, axiom, ![TV_u_27a]: ![V_b, V_a, V_R]: (p(s(t_bool,h4s_relations_strord(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_a),s(TV_u_27a,V_b)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_a))),s(TV_u_27a,V_b)))) & ~ (s(TV_u_27a,V_a) = s(TV_u_27a,V_b))))).
fof(ch4s_enumerals_OUu_u_ASSOC, conjecture, ![TV_u_27a]: ![V_cmp, V_c, V_b, V_a]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_a),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_b),s(t_fun(TV_u_27a,t_bool),V_c))))) = s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_ou(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_a),s(t_fun(TV_u_27a,t_bool),V_b))),s(t_fun(TV_u_27a,t_bool),V_c)))).
