%   ORIGINAL: h4/Omega/final__equivalence
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/LEFT__OR__EXISTS__THM: !Q P. (?x. P x) \/ Q <=> (?x. P x \/ Q)
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/LEFT__FORALL__OR__THM: !Q P. (!x. P x \/ Q) <=> (!x. P x) \/ Q
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/bool/NOT__IMP: !B A. ~(A ==> B) <=> A /\ ~B
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% 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/SKOLEM__THM: !P. (!x. ?y. P x y) <=> (?f. !x. P x (f x))
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/LCOMM__THM: !f. (!x y z. f x (f y z) = f (f x y) z) ==> (!x y. f x y = f y x) ==> (!x y z. f x (f y z) = f y (f x z))
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/marker/AC__DEF: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/NOT__LESS__0: !n. ~h4/prim__rec/_3C n h4/num/0
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% 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/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/FORALL__PROD: !P. (!p. P p) <=> (!p__1 p__2. P (h4/pair/_2C p__1 p__2))
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__RIGHT__1: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = 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/MULT__CLAUSES_c3: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm: h4/arithmetic/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/MULT__EQ__0: !n m. h4/arithmetic/_2A m n = h4/num/0 <=> m = h4/num/0 \/ n = h4/num/0
% Assm: h4/arithmetic/LESS__LESS__EQ__TRANS: !p n m. h4/prim__rec/_3C m n /\ h4/arithmetic/_3C_3D n p ==> h4/prim__rec/_3C m p
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_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__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/EVERY__DEF_c0: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm: h4/list/EVERY__DEF_c1: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> P h /\ h4/list/EVERY P t
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/EVERY__MEM: !l P. h4/list/EVERY P l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> P e)
% Assm: h4/integer/INT__ADD__COMM: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm: h4/integer/INT__MUL__COMM: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm: h4/integer/INT__ADD__ASSOC: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm: h4/integer/INT__MUL__ASSOC: !z y x. h4/integer/int__mul x (h4/integer/int__mul y z) = h4/integer/int__mul (h4/integer/int__mul x y) z
% Assm: h4/integer/INT__LDISTRIB: !z y x. h4/integer/int__mul x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__mul x y) (h4/integer/int__mul x z)
% Assm: h4/integer/INT__LT__REFL: !x. ~h4/integer/int__lt x x
% Assm: h4/integer/INT__LT__TRANS: !z y x. h4/integer/int__lt x y /\ h4/integer/int__lt y z ==> h4/integer/int__lt x z
% Assm: h4/integer/int__sub0: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm: h4/integer/int__ge0: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm: h4/integer/INT__ADD__LID: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm: h4/integer/INT__ADD__RID: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__MUL__LID: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/integer/INT__MUL__RID: !x. h4/integer/int__mul x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm: h4/integer/INT__EQ__RADD: !z y x. h4/integer/int__add x z = h4/integer/int__add y z <=> x = y
% Assm: h4/integer/INT__NEG__LMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm: h4/integer/INT__NEG__RMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm: h4/integer/INT__NEGNEG: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__LT__LADD: !z y x. h4/integer/int__lt (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__lt y z
% Assm: h4/integer/INT__LT__RADD: !z y x. h4/integer/int__lt (h4/integer/int__add x z) (h4/integer/int__add y z) <=> h4/integer/int__lt x y
% Assm: h4/integer/INT__NOT__LT: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm: h4/integer/INT__LT__ANTISYM: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y x)
% Assm: h4/integer/INT__NOT__LE: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm: h4/integer/INT__LE__REFL: !x. h4/integer/int__le x x
% Assm: h4/integer/INT__LE__LT: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm: h4/integer/INT__LT__IMP__LE: !y x. h4/integer/int__lt x y ==> h4/integer/int__le x y
% Assm: h4/integer/INT__LTE__TRANS: !z y x. h4/integer/int__lt x y /\ h4/integer/int__le y z ==> h4/integer/int__lt x z
% Assm: h4/integer/INT__LET__TRANS: !z y x. h4/integer/int__le x y /\ h4/integer/int__lt y z ==> h4/integer/int__lt x z
% Assm: h4/integer/INT__LE__TRANS: !z y x. h4/integer/int__le x y /\ h4/integer/int__le y z ==> h4/integer/int__le x z
% Assm: h4/integer/INT__NEG__LT0: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm: h4/integer/INT__LE__LADD: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Assm: h4/integer/INT__LE__ADD2: !z y x w. h4/integer/int__le w x /\ h4/integer/int__le y z ==> h4/integer/int__le (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm: h4/integer/INT__LT__ADD1: !y x. h4/integer/int__le x y ==> h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/integer/INT__SUB__ADD2: !y x. h4/integer/int__add y (h4/integer/int__sub x y) = x
% Assm: h4/integer/INT__ADD__SUB: !y x. h4/integer/int__sub (h4/integer/int__add x y) x = y
% Assm: h4/integer/INT__SUB__LDISTRIB: !z y x. h4/integer/int__mul x (h4/integer/int__sub y z) = h4/integer/int__sub (h4/integer/int__mul x y) (h4/integer/int__mul x z)
% Assm: h4/integer/INT__SUB__RDISTRIB: !z y x. h4/integer/int__mul (h4/integer/int__sub x y) z = h4/integer/int__sub (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm: h4/integer/INT__LE__ADDR: !y x. h4/integer/int__le x (h4/integer/int__add x y) <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) y
% Assm: h4/integer/INT__LT__ADDR: !y x. h4/integer/int__lt x (h4/integer/int__add x y) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) y
% Assm: h4/integer/INT__LT__ADDL: !y x. h4/integer/int__lt y (h4/integer/int__add x y) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm: h4/integer/INT__EQ__LMUL: !z y x. h4/integer/int__mul x y = h4/integer/int__mul x z <=> x = h4/integer/int__of__num h4/num/0 \/ y = z
% Assm: h4/integer/INT__LE: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/integer/INT__LT: !n m. h4/integer/int__lt (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/prim__rec/_3C m n
% Assm: h4/integer/INT__INJ: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm: h4/integer/INT__MUL: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm: h4/integer/INT__LT__SUB__RADD: !z y x. h4/integer/int__lt (h4/integer/int__sub x y) z <=> h4/integer/int__lt x (h4/integer/int__add z y)
% Assm: h4/integer/INT__LT__SUB__LADD: !z y x. h4/integer/int__lt x (h4/integer/int__sub y z) <=> h4/integer/int__lt (h4/integer/int__add x z) y
% Assm: h4/integer/INT__LE__SUB__LADD: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Assm: h4/integer/INT__LE__SUB__RADD: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm: h4/integer/INT__LE__NEG: !y x. h4/integer/int__le (h4/integer/int__neg x) (h4/integer/int__neg y) <=> h4/integer/int__le y x
% Assm: h4/integer/INT__ADD2__SUB2: !d c b a. h4/integer/int__sub (h4/integer/int__add a b) (h4/integer/int__add c d) = h4/integer/int__add (h4/integer/int__sub a c) (h4/integer/int__sub b d)
% Assm: h4/integer/INT__SUB__LZERO: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm: h4/integer/INT__SUB__RZERO: !x. h4/integer/int__sub x (h4/integer/int__of__num h4/num/0) = x
% Assm: h4/integer/INT__LT__CALCULATE_c0: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__of__num m) <=> h4/prim__rec/_3C n m
% Assm: h4/integer/INT__LT__CALCULATE_c3: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) <=> F
% Assm: h4/integer/NUM__POSINT__EXISTS: !i. h4/integer/int__le (h4/integer/int__of__num h4/num/0) i ==> (?n. i = h4/integer/int__of__num n)
% Assm: h4/integer/INT__DISCRETE: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm: h4/integer/INT__DIV__ID: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__div p p = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/integer/INT__DIVISION: !q. ~(q = h4/integer/int__of__num h4/num/0) ==> (!p. p = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__div p q) q) (h4/integer/int__mod p q) /\ h4/bool/COND (h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)) (h4/integer/int__lt q (h4/integer/int__mod p q) /\ h4/integer/int__le (h4/integer/int__mod p q) (h4/integer/int__of__num h4/num/0)) (h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__mod p q) /\ h4/integer/int__lt (h4/integer/int__mod p q) q))
% Assm: h4/integer/INT__MOD__ID: !i. ~(i = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod i i = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__MOD__COMMON__FACTOR: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> (!q. h4/integer/int__mod (h4/integer/int__mul q p) p = h4/integer/int__of__num h4/num/0)
% Assm: h4/integer/INT__MUL__DIV: !q p k. ~(q = h4/integer/int__of__num h4/num/0) /\ h4/integer/int__mod p q = h4/integer/int__of__num h4/num/0 ==> h4/integer/int__div (h4/integer/int__mul k p) q = h4/integer/int__mul k (h4/integer/int__div p q)
% Assm: h4/integer/INT__ADD__DIV: !k j i. ~(k = h4/integer/int__of__num h4/num/0) /\ (h4/integer/int__mod i k = h4/integer/int__of__num h4/num/0 \/ h4/integer/int__mod j k = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__div (h4/integer/int__add i j) k = h4/integer/int__add (h4/integer/int__div i k) (h4/integer/int__div j k)
% Assm: h4/integer/INT__MUL__SIGN__CASES_c0: !q p. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__mul p q) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) p /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) q \/ h4/integer/int__lt p (h4/integer/int__of__num h4/num/0) /\ h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)
% Assm: h4/integer/INT__LE__CALCULATE: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm: h4/integer/INT__EQ__CALCULATE_c1: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm: h4/integer/INT__EQ__CALCULATE_c2: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm: h4/Omega/fst__nzero__def: !x. h4/Omega/fst__nzero x <=> h4/prim__rec/_3C h4/num/0 (h4/pair/FST x)
% Assm: h4/Omega/dark__shadow__cond__row__tupled__primitive__def: h4/Omega/dark__shadow__cond__row__tupled = h4/relation/WFREC (h4/min/_40 (\R_27. h4/relation/WF R_27 /\ (!R d t L c. R_27 (h4/pair/_2C (h4/pair/_2C c L) t) (h4/pair/_2C (h4/pair/_2C c L) (h4/list/CONS (h4/pair/_2C d R) t))))) (\dark__shadow__cond__row__tupled a. h4/pair/pair__CASE a (\v v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 t. h4/pair/pair__CASE v2 (\d R. h4/pair/pair__CASE v (\c L. h4/combin/I (~(?i. h4/integer/int__lt (h4/integer/int__mul (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) i) (h4/integer/int__mul (h4/integer/int__of__num c) R) /\ h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) R) (h4/integer/int__mul (h4/integer/int__of__num d) L) /\ h4/integer/int__lt (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) /\ dark__shadow__cond__row__tupled (h4/pair/_2C (h4/pair/_2C c L) t)))))))
% Assm: h4/Omega/dark__shadow__cond__row__curried__def: !x1 x. h4/Omega/dark__shadow__cond__row x x1 <=> h4/Omega/dark__shadow__cond__row__tupled (h4/pair/_2C x x1)
% Assm: h4/Omega/dark__shadow__condition__tupled__primitive__def: h4/Omega/dark__shadow__condition__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!L c lowers uppers. R (h4/pair/_2C uppers lowers) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C c L) uppers) lowers)))) (\dark__shadow__condition__tupled a. h4/pair/pair__CASE a (\v lowers. h4/list/list__CASE v (h4/combin/I T) (\v2 uppers. h4/pair/pair__CASE v2 (\c L. h4/combin/I (h4/Omega/dark__shadow__cond__row (h4/pair/_2C c L) lowers /\ dark__shadow__condition__tupled (h4/pair/_2C uppers lowers))))))
% Assm: h4/Omega/dark__shadow__condition__curried__def: !x1 x. h4/Omega/dark__shadow__condition x x1 <=> h4/Omega/dark__shadow__condition__tupled (h4/pair/_2C x x1)
% Assm: h4/Omega/basic__shadow__equivalence: !uppers lowers. h4/list/EVERY h4/Omega/fst__nzero uppers /\ h4/list/EVERY h4/Omega/fst__nzero lowers ==> ((?x. h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) <=> h4/Omega/real__shadow uppers lowers /\ h4/Omega/dark__shadow__condition uppers lowers)
% Assm: h4/Omega/dark__shadow__row__tupled__primitive__def: h4/Omega/dark__shadow__row__tupled = h4/relation/WFREC (h4/min/_40 (\R_27. h4/relation/WF R_27 /\ (!R d rs L c. R_27 (h4/pair/_2C c (h4/pair/_2C L rs)) (h4/pair/_2C c (h4/pair/_2C L (h4/list/CONS (h4/pair/_2C d R) rs)))))) (\dark__shadow__row__tupled a. h4/pair/pair__CASE a (\c v1. h4/pair/pair__CASE v1 (\L v3. h4/list/list__CASE v3 (h4/combin/I T) (\v4 rs. h4/pair/pair__CASE v4 (\d R. h4/combin/I (h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ dark__shadow__row__tupled (h4/pair/_2C c (h4/pair/_2C L rs))))))))
% Assm: h4/Omega/dark__shadow__row__curried__def: !x2 x1 x. h4/Omega/dark__shadow__row x x1 x2 <=> h4/Omega/dark__shadow__row__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/Omega/dark__shadow__tupled__primitive__def: h4/Omega/dark__shadow__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!L c lowers uppers. R (h4/pair/_2C uppers lowers) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C c L) uppers) lowers)))) (\dark__shadow__tupled a. h4/pair/pair__CASE a (\v lowers. h4/list/list__CASE v (h4/combin/I T) (\v2 uppers. h4/pair/pair__CASE v2 (\c L. h4/combin/I (h4/Omega/dark__shadow__row c L lowers /\ dark__shadow__tupled (h4/pair/_2C uppers lowers))))))
% Assm: h4/Omega/dark__shadow__curried__def: !x1 x. h4/Omega/dark__shadow x x1 <=> h4/Omega/dark__shadow__tupled (h4/pair/_2C x x1)
% Assm: h4/Omega/nightmare__implies__LHS: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs ==> h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers
% Assm: h4/Omega/dark__shadow__FORALL: !uppers lowers. h4/Omega/dark__shadow uppers lowers <=> (!c d L R. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm: h4/Omega/evalupper__FORALL: !x uppers. h4/Omega/evalupper x uppers <=> (!c L. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) ==> h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) x) L)
% Assm: h4/Omega/evallower__FORALL: !x lowers. h4/Omega/evallower x lowers <=> (!d R. h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__le R (h4/integer/int__mul (h4/integer/int__of__num d) x))
% Assm: h4/Omega/nightmare__EXISTS: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs <=> (?i d R. h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) (h4/integer/int__of__num c)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET rs) /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i)
% Goal: !uppers m lowers. h4/list/EVERY h4/Omega/fst__nzero uppers /\ h4/list/EVERY h4/Omega/fst__nzero lowers /\ h4/list/EVERY (\p. h4/arithmetic/_3C_3D (h4/pair/FST p) m) uppers ==> ((?x. h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) <=> h4/Omega/real__shadow uppers lowers /\ (h4/Omega/dark__shadow uppers lowers \/ (?x. h4/Omega/nightmare x m uppers lowers lowers)))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_FORALLu_u_ANDu_u_THM]: !Q P. (!x. happ P x /\ happ Q x) <=> (!x. happ P x) /\ (!x. happ Q x)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% 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_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_LEFTu_u_ORu_u_EXISTSu_u_THM]: !Q P. (?x. happ P x) \/ Q <=> (?x. happ P x \/ Q)
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. happ P x \/ Q) <=> (!x. happ P x) \/ Q
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_bools_NOTu_u_IMP]: !B A. ~(A ==> B) <=> A /\ ~B
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_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_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_SKOLEMu_u_THM]: !P. (!x. ?y. happ (happ P x) y) <=> (?f. !x. happ (happ P x) (happ f x))
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_LCOMMu_u_THM]: !f. (!x y z. happ (happ f x) (happ (happ f y) z) = happ (happ f (happ (happ f x) y)) z) ==> (!x y. happ (happ f x) y = happ (happ f y) x) ==> (!x y z. happ (happ f x) (happ (happ f y) z) = happ (happ f y) (happ (happ f x) z))
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_markers_ACu_u_DEF]: !b2 b1. h4/marker/AC b1 b2 <=> b1 /\ b2
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_NOTu_u_LESSu_u_0]: !n. ~happ (happ h4/prim__rec/_3C n) h4/num/0
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% 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_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_FORALLu_u_PROD]: !P. (!p. happ P p) <=> (!p__1 p__2. happ P (h4/pair/_2C p__1 p__2))
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_RIGHTu_u_1]: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = 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_MULTu_u_CLAUSESu_c3]: !m. h4/arithmetic/_2A m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm [h4s_arithmetics_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_MULTu_u_EQu_u_0]: !n m. h4/arithmetic/_2A m n = h4/num/0 <=> m = h4/num/0 \/ n = h4/num/0
% Assm [h4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS]: !p n m. happ (happ h4/prim__rec/_3C m) n /\ h4/arithmetic/_3C_3D n p ==> happ (happ h4/prim__rec/_3C m) p
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_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_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_EVERYu_u_DEFu_c0]: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm [h4s_lists_EVERYu_u_DEFu_c1]: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> happ P h /\ h4/list/EVERY P t
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_EVERYu_u_MEM]: !l P. h4/list/EVERY P l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> happ P e)
% Assm [h4s_integers_INTu_u_ADDu_u_COMM]: !y x. h4/integer/int__add x y = h4/integer/int__add y x
% Assm [h4s_integers_INTu_u_MULu_u_COMM]: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm [h4s_integers_INTu_u_ADDu_u_ASSOC]: !z y x. h4/integer/int__add x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__add x y) z
% Assm [h4s_integers_INTu_u_MULu_u_ASSOC]: !z y x. h4/integer/int__mul x (h4/integer/int__mul y z) = h4/integer/int__mul (h4/integer/int__mul x y) z
% Assm [h4s_integers_INTu_u_LDISTRIB]: !z y x. h4/integer/int__mul x (h4/integer/int__add y z) = h4/integer/int__add (h4/integer/int__mul x y) (h4/integer/int__mul x z)
% Assm [h4s_integers_INTu_u_LTu_u_REFL]: !x. ~h4/integer/int__lt x x
% Assm [h4s_integers_INTu_u_LTu_u_TRANS]: !z y x. h4/integer/int__lt x y /\ h4/integer/int__lt y z ==> h4/integer/int__lt x z
% Assm [h4s_integers_intu_u_sub0]: !y x. h4/integer/int__sub x y = h4/integer/int__add x (h4/integer/int__neg y)
% Assm [h4s_integers_intu_u_ge0]: !y x. h4/integer/int__ge x y <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_ADDu_u_LID]: !x. h4/integer/int__add (h4/integer/int__of__num h4/num/0) x = x
% Assm [h4s_integers_INTu_u_ADDu_u_RID]: !x. h4/integer/int__add x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_MULu_u_LID]: !x. h4/integer/int__mul (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_integers_INTu_u_MULu_u_RID]: !x. h4/integer/int__mul x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm [h4s_integers_INTu_u_EQu_u_RADD]: !z y x. h4/integer/int__add x z = h4/integer/int__add y z <=> x = y
% Assm [h4s_integers_INTu_u_NEGu_u_LMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm [h4s_integers_INTu_u_NEGu_u_RMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_NEGNEG]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_LTu_u_LADD]: !z y x. h4/integer/int__lt (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__lt y z
% Assm [h4s_integers_INTu_u_LTu_u_RADD]: !z y x. h4/integer/int__lt (h4/integer/int__add x z) (h4/integer/int__add y z) <=> h4/integer/int__lt x y
% Assm [h4s_integers_INTu_u_NOTu_u_LT]: !y x. ~h4/integer/int__lt x y <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_LTu_u_ANTISYM]: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y x)
% Assm [h4s_integers_INTu_u_NOTu_u_LE]: !y x. ~h4/integer/int__le x y <=> h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LEu_u_REFL]: !x. h4/integer/int__le x x
% Assm [h4s_integers_INTu_u_LEu_u_LT]: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm [h4s_integers_INTu_u_LTu_u_IMPu_u_LE]: !y x. h4/integer/int__lt x y ==> h4/integer/int__le x y
% Assm [h4s_integers_INTu_u_LTEu_u_TRANS]: !z y x. h4/integer/int__lt x y /\ h4/integer/int__le y z ==> h4/integer/int__lt x z
% Assm [h4s_integers_INTu_u_LETu_u_TRANS]: !z y x. h4/integer/int__le x y /\ h4/integer/int__lt y z ==> h4/integer/int__lt x z
% Assm [h4s_integers_INTu_u_LEu_u_TRANS]: !z y x. h4/integer/int__le x y /\ h4/integer/int__le y z ==> h4/integer/int__le x z
% Assm [h4s_integers_INTu_u_NEGu_u_LT0]: !x. h4/integer/int__lt (h4/integer/int__neg x) (h4/integer/int__of__num h4/num/0) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm [h4s_integers_INTu_u_LEu_u_LADD]: !z y x. h4/integer/int__le (h4/integer/int__add x y) (h4/integer/int__add x z) <=> h4/integer/int__le y z
% Assm [h4s_integers_INTu_u_LEu_u_ADD2]: !z y x w. h4/integer/int__le w x /\ h4/integer/int__le y z ==> h4/integer/int__le (h4/integer/int__add w y) (h4/integer/int__add x z)
% Assm [h4s_integers_INTu_u_LTu_u_ADD1]: !y x. h4/integer/int__le x y ==> h4/integer/int__lt x (h4/integer/int__add y (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_integers_INTu_u_SUBu_u_ADD2]: !y x. h4/integer/int__add y (h4/integer/int__sub x y) = x
% Assm [h4s_integers_INTu_u_ADDu_u_SUB]: !y x. h4/integer/int__sub (h4/integer/int__add x y) x = y
% Assm [h4s_integers_INTu_u_SUBu_u_LDISTRIB]: !z y x. h4/integer/int__mul x (h4/integer/int__sub y z) = h4/integer/int__sub (h4/integer/int__mul x y) (h4/integer/int__mul x z)
% Assm [h4s_integers_INTu_u_SUBu_u_RDISTRIB]: !z y x. h4/integer/int__mul (h4/integer/int__sub x y) z = h4/integer/int__sub (h4/integer/int__mul x z) (h4/integer/int__mul y z)
% Assm [h4s_integers_INTu_u_LEu_u_ADDR]: !y x. h4/integer/int__le x (h4/integer/int__add x y) <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) y
% Assm [h4s_integers_INTu_u_LTu_u_ADDR]: !y x. h4/integer/int__lt x (h4/integer/int__add x y) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) y
% Assm [h4s_integers_INTu_u_LTu_u_ADDL]: !y x. h4/integer/int__lt y (h4/integer/int__add x y) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x
% Assm [h4s_integers_INTu_u_EQu_u_LMUL]: !z y x. h4/integer/int__mul x y = h4/integer/int__mul x z <=> x = h4/integer/int__of__num h4/num/0 \/ y = z
% Assm [h4s_integers_INTu_u_LE]: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_integers_INTu_u_LT]: !n m. h4/integer/int__lt (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_integers_INTu_u_INJ]: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm [h4s_integers_INTu_u_MUL]: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm [h4s_integers_INTu_u_LTu_u_SUBu_u_RADD]: !z y x. h4/integer/int__lt (h4/integer/int__sub x y) z <=> h4/integer/int__lt x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_LTu_u_SUBu_u_LADD]: !z y x. h4/integer/int__lt x (h4/integer/int__sub y z) <=> h4/integer/int__lt (h4/integer/int__add x z) y
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_LADD]: !z y x. h4/integer/int__le x (h4/integer/int__sub y z) <=> h4/integer/int__le (h4/integer/int__add x z) y
% Assm [h4s_integers_INTu_u_LEu_u_SUBu_u_RADD]: !z y x. h4/integer/int__le (h4/integer/int__sub x y) z <=> h4/integer/int__le x (h4/integer/int__add z y)
% Assm [h4s_integers_INTu_u_LEu_u_NEG]: !y x. h4/integer/int__le (h4/integer/int__neg x) (h4/integer/int__neg y) <=> h4/integer/int__le y x
% Assm [h4s_integers_INTu_u_ADD2u_u_SUB2]: !d c b a. h4/integer/int__sub (h4/integer/int__add a b) (h4/integer/int__add c d) = h4/integer/int__add (h4/integer/int__sub a c) (h4/integer/int__sub b d)
% Assm [h4s_integers_INTu_u_SUBu_u_LZERO]: !x. h4/integer/int__sub (h4/integer/int__of__num h4/num/0) x = h4/integer/int__neg x
% Assm [h4s_integers_INTu_u_SUBu_u_RZERO]: !x. h4/integer/int__sub x (h4/integer/int__of__num h4/num/0) = x
% Assm [h4s_integers_INTu_u_LTu_u_CALCULATEu_c0]: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__of__num m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_integers_INTu_u_LTu_u_CALCULATEu_c3]: !n m. h4/integer/int__lt (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) <=> F
% Assm [h4s_integers_NUMu_u_POSINTu_u_EXISTS]: !i. h4/integer/int__le (h4/integer/int__of__num h4/num/0) i ==> (?n. i = h4/integer/int__of__num n)
% Assm [h4s_integers_INTu_u_DISCRETE]: !y x. ~(h4/integer/int__lt x y /\ h4/integer/int__lt y (h4/integer/int__add x (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))
% Assm [h4s_integers_INTu_u_DIVu_u_ID]: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__div p p = h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_integers_INTu_u_DIVISION]: !q. ~(q = h4/integer/int__of__num h4/num/0) ==> (!p. p = h4/integer/int__add (h4/integer/int__mul (h4/integer/int__div p q) q) (h4/integer/int__mod p q) /\ (?v. (v <=> h4/integer/int__lt q (h4/integer/int__mod p q) /\ h4/integer/int__le (h4/integer/int__mod p q) (h4/integer/int__of__num h4/num/0)) /\ (?v'. (v' <=> h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer/int__mod p q) /\ h4/integer/int__lt (h4/integer/int__mod p q) q) /\ h4/bool/COND (h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)) v v')))
% Assm [h4s_integers_INTu_u_MODu_u_ID]: !i. ~(i = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod i i = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_MODu_u_COMMONu_u_FACTOR]: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> (!q. h4/integer/int__mod (h4/integer/int__mul q p) p = h4/integer/int__of__num h4/num/0)
% Assm [h4s_integers_INTu_u_MULu_u_DIV]: !q p k. ~(q = h4/integer/int__of__num h4/num/0) /\ h4/integer/int__mod p q = h4/integer/int__of__num h4/num/0 ==> h4/integer/int__div (h4/integer/int__mul k p) q = h4/integer/int__mul k (h4/integer/int__div p q)
% Assm [h4s_integers_INTu_u_ADDu_u_DIV]: !k j i. ~(k = h4/integer/int__of__num h4/num/0) /\ (h4/integer/int__mod i k = h4/integer/int__of__num h4/num/0 \/ h4/integer/int__mod j k = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__div (h4/integer/int__add i j) k = h4/integer/int__add (h4/integer/int__div i k) (h4/integer/int__div j k)
% Assm [h4s_integers_INTu_u_MULu_u_SIGNu_u_CASESu_c0]: !q p. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__mul p q) <=> h4/integer/int__lt (h4/integer/int__of__num h4/num/0) p /\ h4/integer/int__lt (h4/integer/int__of__num h4/num/0) q \/ h4/integer/int__lt p (h4/integer/int__of__num h4/num/0) /\ h4/integer/int__lt q (h4/integer/int__of__num h4/num/0)
% Assm [h4s_integers_INTu_u_LEu_u_CALCULATE]: !y x. h4/integer/int__le x y <=> h4/integer/int__lt x y \/ x = y
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c1]: !y x. h4/integer/int__neg x = h4/integer/int__neg y <=> x = y
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c2]: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm [h4s_Omegas_fstu_u_nzerou_u_def]: !x. happ h4/Omega/fst__nzero x <=> happ (happ h4/prim__rec/_3C h4/num/0) (h4/pair/FST x)
% Assm [h4s_Omegas_darku_u_shadowu_u_condu_u_rowu_u_tupledu_u_primitiveu_u_def]: !_10. (!R d dark__shadow__cond__row__tupled c t L. ?v. (v <=> ~(?i. h4/integer/int__lt (h4/integer/int__mul (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) i) (h4/integer/int__mul (h4/integer/int__of__num c) R) /\ h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) R) (h4/integer/int__mul (h4/integer/int__of__num d) L) /\ h4/integer/int__lt (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__add i (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) /\ happ dark__shadow__cond__row__tupled (h4/pair/_2C (h4/pair/_2C c L) t)) /\ (happ (happ (happ (happ (happ (happ _10 R) d) dark__shadow__cond__row__tupled) c) t) L <=> h4/combin/I v)) ==> (!_9. (!R d dark__shadow__cond__row__tupled t c. happ (happ (happ (happ (happ _9 R) d) dark__shadow__cond__row__tupled) t) c = happ (happ (happ (happ (happ _10 R) d) dark__shadow__cond__row__tupled) c) t) ==> (!_8. (!v d dark__shadow__cond__row__tupled t R. happ (happ (happ (happ (happ _8 v) d) dark__shadow__cond__row__tupled) t) R <=> h4/pair/pair__CASE v (happ (happ (happ (happ _9 R) d) dark__shadow__cond__row__tupled) t)) ==> (!_7. (!v dark__shadow__cond__row__tupled t d. happ (happ (happ (happ _7 v) dark__shadow__cond__row__tupled) t) d = happ (happ (happ (happ _8 v) d) dark__shadow__cond__row__tupled) t) ==> (!_6. (!v2 v dark__shadow__cond__row__tupled t. happ (happ (happ (happ _6 v2) v) dark__shadow__cond__row__tupled) t <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 v) dark__shadow__cond__row__tupled) t)) ==> (!_5. (!v dark__shadow__cond__row__tupled v2. happ (happ (happ _5 v) dark__shadow__cond__row__tupled) v2 = happ (happ (happ _6 v2) v) dark__shadow__cond__row__tupled) ==> (!_4. (!v dark__shadow__cond__row__tupled v1. happ (happ (happ _4 v) dark__shadow__cond__row__tupled) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 v) dark__shadow__cond__row__tupled)) ==> (!_3. (!dark__shadow__cond__row__tupled v. happ (happ _3 dark__shadow__cond__row__tupled) v = happ (happ _4 v) dark__shadow__cond__row__tupled) ==> (!_2. (!dark__shadow__cond__row__tupled a. happ (happ _2 dark__shadow__cond__row__tupled) a <=> h4/pair/pair__CASE a (happ _3 dark__shadow__cond__row__tupled)) ==> (!_1. (!dark__shadow__cond__row__tupled. happ _1 dark__shadow__cond__row__tupled = happ _2 dark__shadow__cond__row__tupled) ==> (!_0. (!R_27. happ _0 R_27 <=> h4/relation/WF R_27 /\ (!R d t L c. happ (happ R_27 (h4/pair/_2C (h4/pair/_2C c L) t)) (h4/pair/_2C (h4/pair/_2C c L) (h4/list/CONS (h4/pair/_2C d R) t)))) ==> h4/Omega/dark__shadow__cond__row__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_Omegas_darku_u_shadowu_u_condu_u_rowu_u_curriedu_u_def]: !x1 x. h4/Omega/dark__shadow__cond__row x x1 <=> happ h4/Omega/dark__shadow__cond__row__tupled (h4/pair/_2C x x1)
% Assm [h4s_Omegas_darku_u_shadowu_u_conditionu_u_tupledu_u_primitiveu_u_def]: !_8. (!c dark__shadow__condition__tupled uppers lowers L. ?v. (v <=> h4/Omega/dark__shadow__cond__row (h4/pair/_2C c L) lowers /\ happ dark__shadow__condition__tupled (h4/pair/_2C uppers lowers)) /\ (happ (happ (happ (happ (happ _8 c) dark__shadow__condition__tupled) uppers) lowers) L <=> h4/combin/I v)) ==> (!_7. (!dark__shadow__condition__tupled uppers lowers c. happ (happ (happ (happ _7 dark__shadow__condition__tupled) uppers) lowers) c = happ (happ (happ (happ _8 c) dark__shadow__condition__tupled) uppers) lowers) ==> (!_6. (!v2 dark__shadow__condition__tupled lowers uppers. happ (happ (happ (happ _6 v2) dark__shadow__condition__tupled) lowers) uppers <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 dark__shadow__condition__tupled) uppers) lowers)) ==> (!_5. (!dark__shadow__condition__tupled lowers v2. happ (happ (happ _5 dark__shadow__condition__tupled) lowers) v2 = happ (happ (happ _6 v2) dark__shadow__condition__tupled) lowers) ==> (!_4. (!v dark__shadow__condition__tupled lowers. happ (happ (happ _4 v) dark__shadow__condition__tupled) lowers <=> h4/list/list__CASE v (h4/combin/I T) (happ (happ _5 dark__shadow__condition__tupled) lowers)) ==> (!_3. (!dark__shadow__condition__tupled v. happ (happ _3 dark__shadow__condition__tupled) v = happ (happ _4 v) dark__shadow__condition__tupled) ==> (!_2. (!dark__shadow__condition__tupled a. happ (happ _2 dark__shadow__condition__tupled) a <=> h4/pair/pair__CASE a (happ _3 dark__shadow__condition__tupled)) ==> (!_1. (!dark__shadow__condition__tupled. happ _1 dark__shadow__condition__tupled = happ _2 dark__shadow__condition__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!L c lowers uppers. happ (happ R (h4/pair/_2C uppers lowers)) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C c L) uppers) lowers))) ==> h4/Omega/dark__shadow__condition__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_Omegas_darku_u_shadowu_u_conditionu_u_curriedu_u_def]: !x1 x. h4/Omega/dark__shadow__condition x x1 <=> happ h4/Omega/dark__shadow__condition__tupled (h4/pair/_2C x x1)
% Assm [h4s_Omegas_basicu_u_shadowu_u_equivalence]: !uppers lowers. h4/list/EVERY h4/Omega/fst__nzero uppers /\ h4/list/EVERY h4/Omega/fst__nzero lowers ==> ((?x. h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) <=> h4/Omega/real__shadow uppers lowers /\ h4/Omega/dark__shadow__condition uppers lowers)
% Assm [h4s_Omegas_darku_u_shadowu_u_rowu_u_tupledu_u_primitiveu_u_def]: !_10. (!d dark__shadow__row__tupled c L rs R. ?v. (v <=> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) /\ happ dark__shadow__row__tupled (h4/pair/_2C c (h4/pair/_2C L rs))) /\ (happ (happ (happ (happ (happ (happ _10 d) dark__shadow__row__tupled) c) L) rs) R <=> h4/combin/I v)) ==> (!_9. (!dark__shadow__row__tupled c L rs d. happ (happ (happ (happ (happ _9 dark__shadow__row__tupled) c) L) rs) d = happ (happ (happ (happ (happ _10 d) dark__shadow__row__tupled) c) L) rs) ==> (!_8. (!v4 dark__shadow__row__tupled c L rs. happ (happ (happ (happ (happ _8 v4) dark__shadow__row__tupled) c) L) rs <=> h4/pair/pair__CASE v4 (happ (happ (happ (happ _9 dark__shadow__row__tupled) c) L) rs)) ==> (!_7. (!dark__shadow__row__tupled c L v4. happ (happ (happ (happ _7 dark__shadow__row__tupled) c) L) v4 = happ (happ (happ (happ _8 v4) dark__shadow__row__tupled) c) L) ==> (!_6. (!dark__shadow__row__tupled c L v3. happ (happ (happ (happ _6 dark__shadow__row__tupled) c) L) v3 <=> h4/list/list__CASE v3 (h4/combin/I T) (happ (happ (happ _7 dark__shadow__row__tupled) c) L)) ==> (!_5. (!dark__shadow__row__tupled c L. happ (happ (happ _5 dark__shadow__row__tupled) c) L = happ (happ (happ _6 dark__shadow__row__tupled) c) L) ==> (!_4. (!dark__shadow__row__tupled c v1. happ (happ (happ _4 dark__shadow__row__tupled) c) v1 <=> h4/pair/pair__CASE v1 (happ (happ _5 dark__shadow__row__tupled) c)) ==> (!_3. (!dark__shadow__row__tupled c. happ (happ _3 dark__shadow__row__tupled) c = happ (happ _4 dark__shadow__row__tupled) c) ==> (!_2. (!dark__shadow__row__tupled a. happ (happ _2 dark__shadow__row__tupled) a <=> h4/pair/pair__CASE a (happ _3 dark__shadow__row__tupled)) ==> (!_1. (!dark__shadow__row__tupled. happ _1 dark__shadow__row__tupled = happ _2 dark__shadow__row__tupled) ==> (!_0. (!R_27. happ _0 R_27 <=> h4/relation/WF R_27 /\ (!R d rs L c. happ (happ R_27 (h4/pair/_2C c (h4/pair/_2C L rs))) (h4/pair/_2C c (h4/pair/_2C L (h4/list/CONS (h4/pair/_2C d R) rs))))) ==> h4/Omega/dark__shadow__row__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_Omegas_darku_u_shadowu_u_rowu_u_curriedu_u_def]: !x2 x1 x. h4/Omega/dark__shadow__row x x1 x2 <=> happ h4/Omega/dark__shadow__row__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_Omegas_darku_u_shadowu_u_tupledu_u_primitiveu_u_def]: !_8. (!c dark__shadow__tupled uppers lowers L. ?v. (v <=> h4/Omega/dark__shadow__row c L lowers /\ happ dark__shadow__tupled (h4/pair/_2C uppers lowers)) /\ (happ (happ (happ (happ (happ _8 c) dark__shadow__tupled) uppers) lowers) L <=> h4/combin/I v)) ==> (!_7. (!dark__shadow__tupled uppers lowers c. happ (happ (happ (happ _7 dark__shadow__tupled) uppers) lowers) c = happ (happ (happ (happ _8 c) dark__shadow__tupled) uppers) lowers) ==> (!_6. (!v2 dark__shadow__tupled lowers uppers. happ (happ (happ (happ _6 v2) dark__shadow__tupled) lowers) uppers <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 dark__shadow__tupled) uppers) lowers)) ==> (!_5. (!dark__shadow__tupled lowers v2. happ (happ (happ _5 dark__shadow__tupled) lowers) v2 = happ (happ (happ _6 v2) dark__shadow__tupled) lowers) ==> (!_4. (!v dark__shadow__tupled lowers. happ (happ (happ _4 v) dark__shadow__tupled) lowers <=> h4/list/list__CASE v (h4/combin/I T) (happ (happ _5 dark__shadow__tupled) lowers)) ==> (!_3. (!dark__shadow__tupled v. happ (happ _3 dark__shadow__tupled) v = happ (happ _4 v) dark__shadow__tupled) ==> (!_2. (!dark__shadow__tupled a. happ (happ _2 dark__shadow__tupled) a <=> h4/pair/pair__CASE a (happ _3 dark__shadow__tupled)) ==> (!_1. (!dark__shadow__tupled. happ _1 dark__shadow__tupled = happ _2 dark__shadow__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!L c lowers uppers. happ (happ R (h4/pair/_2C uppers lowers)) (h4/pair/_2C (h4/list/CONS (h4/pair/_2C c L) uppers) lowers))) ==> h4/Omega/dark__shadow__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_Omegas_darku_u_shadowu_u_curriedu_u_def]: !x1 x. h4/Omega/dark__shadow x x1 <=> happ h4/Omega/dark__shadow__tupled (h4/pair/_2C x x1)
% Assm [h4s_Omegas_nightmareu_u_impliesu_u_LHS]: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs ==> h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers
% Assm [h4s_Omegas_darku_u_shadowu_u_FORALL]: !uppers lowers. h4/Omega/dark__shadow uppers lowers <=> (!c d L R. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__ge (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) L) (h4/integer/int__mul (h4/integer/int__of__num c) R)) (h4/integer/int__mul (h4/integer/int__sub (h4/integer/int__of__num c) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/integer/int__sub (h4/integer/int__of__num d) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm [h4s_Omegas_evalupperu_u_FORALL]: !x uppers. h4/Omega/evalupper x uppers <=> (!c L. h4/bool/IN (h4/pair/_2C c L) (h4/list/LIST__TO__SET uppers) ==> h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) x) L)
% Assm [h4s_Omegas_evalloweru_u_FORALL]: !x lowers. h4/Omega/evallower x lowers <=> (!d R. h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET lowers) ==> h4/integer/int__le R (h4/integer/int__mul (h4/integer/int__of__num d) x))
% Assm [h4s_Omegas_nightmareu_u_EXISTS]: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs <=> (?i d R. h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num d) (h4/integer/int__of__num c)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) /\ h4/bool/IN (h4/pair/_2C d R) (h4/list/LIST__TO__SET rs) /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i)
% Goal: !_0. (!m p. happ (happ _0 m) p <=> h4/arithmetic/_3C_3D (h4/pair/FST p) m) ==> (!uppers m lowers. h4/list/EVERY h4/Omega/fst__nzero uppers /\ h4/list/EVERY h4/Omega/fst__nzero lowers /\ h4/list/EVERY (happ _0 m) uppers ==> ((?x. h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) <=> h4/Omega/real__shadow uppers lowers /\ (h4/Omega/dark__shadow uppers lowers \/ (?x. h4/Omega/nightmare x m uppers lowers lowers))))
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_Q19176,TV_Q19172]: ![V_f, V_g]: (![V_x]: s(TV_Q19172,happ(s(t_fun(TV_Q19176,TV_Q19172),V_f),s(TV_Q19176,V_x))) = s(TV_Q19172,happ(s(t_fun(TV_Q19176,TV_Q19172),V_g),s(TV_Q19176,V_x))) => s(t_fun(TV_Q19176,TV_Q19172),V_f) = s(t_fun(TV_Q19176,TV_Q19172),V_g))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_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_bools_TRUTH, axiom, p(s(t_bool,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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_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_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
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_ANDu_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_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_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_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_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,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_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_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_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_FORALLu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (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_Q),s(TV_u_27a,V_x))))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![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_bools_LEFTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((![V_x]: 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,V_Q))) <=> ![V_x]: (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,V_Q))))).
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_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (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_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[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_bools_LEFTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((?[V_x]: 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,V_Q))) <=> ?[V_x]: (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,V_Q))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_EXISTSu_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_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (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,V_Q))) <=> (?[V_x]: 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,V_Q))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_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_bools_LEFTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (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,V_Q))) <=> (![V_x]: 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,V_Q))))).
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_bools_NOTu_u_IMP, 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_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_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_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_SKOLEMu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (![V_x]: ?[V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> ?[V_f]: ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),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_bools_boolu_u_caseu_u_thmu_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_bools_LCOMMu_u_THM, axiom, ![TV_u_27a]: ![V_f]: (![V_x, V_y, V_z]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))),s(TV_u_27a,V_z))) => (![V_x, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_x))) => ![V_x, V_y, V_z]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_z)))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_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_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_abbrev(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_markers_ACu_u_DEF, axiom, ![V_b2, V_b1]: (p(s(t_bool,h4s_markers_ac(s(t_bool,V_b1),s(t_bool,V_b2)))) <=> (p(s(t_bool,V_b1)) & p(s(t_bool,V_b2))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: 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)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(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_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (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_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(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),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_NOTu_u_LESSu_u_0, axiom, ![V_n]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
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_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_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_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_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),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_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_pairs_FORALLu_u_PROD, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: (![V_p]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p)))) <=> ![V_pu_u_1, V_pu_u_2]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_pu_u_1),s(TV_u_27b,V_pu_u_2)))))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_RIGHTu_u_1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),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)).
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_MULTu_u_CLAUSESu_c3, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),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)).
fof(ah4s_arithmetics_MULTu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_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_MULTu_u_EQu_u_0, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) | s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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_p))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_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_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_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = 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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_EVERYu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_lists_EVERYu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) & p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_EVERYu_u_MEM, axiom, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> ![V_e]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),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,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_e))))))).
fof(ah4s_integers_INTu_u_ADDu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_MULu_u_COMM, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_MULu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LTu_u_REFL, axiom, ![V_x]: ~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_LTu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_intu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_intu_u_ge0, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADDu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,V_x))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,V_x)).
fof(ah4s_integers_INTu_u_EQu_u_RADD, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y))).
fof(ah4s_integers_INTu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NEGu_u_RMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_LTu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_LTu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_LTu_u_ANTISYM, axiom, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x))))))).
fof(ah4s_integers_INTu_u_NOTu_u_LE, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) <=> p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))))).
fof(ah4s_integers_INTu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_x))))).
fof(ah4s_integers_INTu_u_LEu_u_LT, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) | s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LTu_u_IMPu_u_LE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LTEu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LETu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LEu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_NEGu_u_LT0, axiom, ![V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LEu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_LEu_u_ADD2, axiom, ![V_z, V_y, V_x, V_w]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_x)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_w),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))))).
fof(ah4s_integers_INTu_u_LTu_u_ADD1, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) => p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))).
fof(ah4s_integers_INTu_u_SUBu_u_ADD2, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_ADDu_u_SUB, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,V_y)).
fof(ah4s_integers_INTu_u_SUBu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_SUBu_u_RDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z)))))).
fof(ah4s_integers_INTu_u_LEu_u_ADDR, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LTu_u_ADDR, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LTu_u_ADDL, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_EQu_u_LMUL, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))) <=> (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_integers_int,V_y) = s(t_h4s_integers_int,V_z)))).
fof(ah4s_integers_INTu_u_LE, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_LT, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_integers_INTu_u_INJ, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_integers_INTu_u_MUL, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_integers_INTu_u_LTu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LTu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_LEu_u_SUBu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))),s(t_h4s_integers_int,V_z))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_z),s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_LEu_u_NEG, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))))) = s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_ADD2u_u_SUB2, axiom, ![V_d, V_c, V_b, V_a]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_b))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_c),s(t_h4s_integers_int,V_d))))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_b),s(t_h4s_integers_int,V_d)))))).
fof(ah4s_integers_INTu_u_SUBu_u_LZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_SUBu_u_RZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_bool,f)).
fof(ah4s_integers_NUMu_u_POSINTu_u_EXISTS, axiom, ![V_i]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))) => ?[V_n]: s(t_h4s_integers_int,V_i) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))).
fof(ah4s_integers_INTu_u_DISCRETE, axiom, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))).
fof(ah4s_integers_INTu_u_DIVu_u_ID, axiom, ![V_p]: (~ (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_p))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_integers_INTu_u_DIVISION, axiom, ![V_q]: (~ (s(t_h4s_integers_int,V_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ![V_p]: (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))))) & ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))),s(t_h4s_integers_int,V_q)))))) & p(s(t_bool,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_bool,V_v),s(t_bool,V_vi_))))))))).
fof(ah4s_integers_INTu_u_MODu_u_ID, axiom, ![V_i]: (~ (s(t_h4s_integers_int,V_i) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_i))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_integers_INTu_u_MODu_u_COMMONu_u_FACTOR, axiom, ![V_p]: (~ (s(t_h4s_integers_int,V_p) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ![V_q]: s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_p))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_integers_INTu_u_MULu_u_DIV, axiom, ![V_q, V_p, V_k]: ((~ (s(t_h4s_integers_int,V_q) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_q))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_k),s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q))))))).
fof(ah4s_integers_INTu_u_ADDu_u_DIV, axiom, ![V_k, V_j, V_i]: ((~ (s(t_h4s_integers_int,V_k) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & (s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_k))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_k))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) => s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_j))),s(t_h4s_integers_int,V_k))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,V_k))),s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,V_j),s(t_h4s_integers_int,V_k))))))).
fof(ah4s_integers_INTu_u_MULu_u_SIGNu_u_CASESu_c0, axiom, ![V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))))) <=> ((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_p)))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_q))))) | (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_integers_INTu_u_LEu_u_CALCULATE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) <=> (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y)))) | s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c1, axiom, ![V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y))) <=> s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,V_y))).
fof(ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) <=> (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_Omegas_fstu_u_nzerou_u_def, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_bool),h4s_omegas_fstu_u_nzero),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),V_x)))))).
fof(ah4s_Omegas_darku_u_shadowu_u_condu_u_rowu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_10]: (![V_R, V_d, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_c, V_t, V_L]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (~ (?[V_i]: (p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,V_i))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_R)))))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_R))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_L)))))) & p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_L))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t)))))))) & s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_integers_int,V_R))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))),s(t_h4s_integers_int,V_L))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_9]: (![V_R, V_d, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_t, V_c]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_h4s_integers_int,V_R))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))),s(t_h4s_nums_num,V_c))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_integers_int,V_R))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))) => ![V_uu_8]: (![V_v, V_d, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_t, V_R]: s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))),s(t_h4s_integers_int,V_R))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_h4s_integers_int,V_R))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))))) => ![V_uu_7]: (![V_v, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_t, V_d]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))),s(t_h4s_nums_num,V_d))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))) => ![V_uu_6]: (![V_v2, V_v, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_t]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))))) => ![V_uu_5]: (![V_v, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))) => ![V_uu_4]: (![V_v, V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v1))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v1),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))))) => ![V_uu_3]: (![V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_v]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))) => ![V_uu_2]: (![V_darku_u_shadowu_u_condu_u_rowu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))))) => ![V_uu_1]: (![V_darku_u_shadowu_u_condu_u_rowu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_condu_u_rowu_u_tupled))) => ![V_uu_0]: (![V_Ru_27]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_Ru_27)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_Ru_27)))) & ![V_R, V_d, V_t, V_L, V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_Ru_27),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t))))),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_t)))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_condu_u_rowu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1))))))))))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_condu_u_rowu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_bool,h4s_omegas_darku_u_shadowu_u_condu_u_row(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_condu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1)))))).
fof(ah4s_Omegas_darku_u_shadowu_u_conditionu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_c, V_darku_u_shadowu_u_conditionu_u_tupled, V_uppers, V_lowers, V_L]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_omegas_darku_u_shadowu_u_condu_u_row(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))) & s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_nums_num,V_c))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_integers_int,V_L))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_darku_u_shadowu_u_conditionu_u_tupled, V_uppers, V_lowers, V_c]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_nums_num,V_c))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_nums_num,V_c))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_6]: (![V_v2, V_darku_u_shadowu_u_conditionu_u_tupled, V_lowers, V_uppers]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => ![V_uu_5]: (![V_darku_u_shadowu_u_conditionu_u_tupled, V_lowers, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_4]: (![V_v, V_darku_u_shadowu_u_conditionu_u_tupled, V_lowers]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => ![V_uu_3]: (![V_darku_u_shadowu_u_conditionu_u_tupled, V_v]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))) => ![V_uu_2]: (![V_darku_u_shadowu_u_conditionu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))))) => ![V_uu_1]: (![V_darku_u_shadowu_u_conditionu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_conditionu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R)))) & ![V_L, V_c, V_lowers, V_uppers]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_conditionu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1))))))))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_conditionu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_bool,h4s_omegas_darku_u_shadowu_u_condition(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_conditionu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1)))))).
fof(ah4s_Omegas_basicu_u_shadowu_u_equivalence, axiom, ![V_uppers, V_lowers]: ((p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_omegas_fstu_u_nzero),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_omegas_fstu_u_nzero),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => (?[V_x]: (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) <=> (p(s(t_bool,h4s_omegas_realu_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & p(s(t_bool,h4s_omegas_darku_u_shadowu_u_condition(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_rowu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_10]: (![V_d, V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs, V_R]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_L))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_R))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))) & p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))))))) & s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_integers_int,V_R))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_9]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs, V_d]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_nums_num,V_d))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))))),V_uu_10),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_8]: (![V_v4, V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_rs]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_7]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_v4]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_8),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v4))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) => ![V_uu_6]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L, V_v3]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v3))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v3),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))))) => ![V_uu_5]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_L]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_L))) => ![V_uu_4]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_v1))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_v1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))))) => ![V_uu_3]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_c]: s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_c))) => ![V_uu_2]: (![V_darku_u_shadowu_u_rowu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),V_a),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))))) => ![V_uu_1]: (![V_darku_u_shadowu_u_rowu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_darku_u_shadowu_u_rowu_u_tupled))) => ![V_uu_0]: (![V_Ru_27]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27)))) & ![V_R, V_d, V_rs, V_L, V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_Ru_27),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_darku_u_shadowu_u_rowu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_1))))))))))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_rowu_u_curriedu_u_def, axiom, ![V_x2, V_x1, V_x]: s(t_bool,h4s_omegas_darku_u_shadowu_u_row(s(t_h4s_nums_num,V_x),s(t_h4s_integers_int,V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_darku_u_shadowu_u_rowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_integers_int,V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2)))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_c, V_darku_u_shadowu_u_tupled, V_uppers, V_lowers, V_L]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_omegas_darku_u_shadowu_u_row(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))) & s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_nums_num,V_c))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_integers_int,V_L))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_darku_u_shadowu_u_tupled, V_uppers, V_lowers, V_c]: s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_nums_num,V_c))) = s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_integers_int,t_bool))))),V_uu_8),s(t_h4s_nums_num,V_c))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_6]: (![V_v2, V_darku_u_shadowu_u_tupled, V_lowers, V_uppers]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_nums_num,t_fun(t_h4s_integers_int,t_bool))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => ![V_uu_5]: (![V_darku_u_shadowu_u_tupled, V_lowers, V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_4]: (![V_v, V_darku_u_shadowu_u_tupled, V_lowers]: s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) = s(t_bool,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v),s(t_bool,h4s_combins_i(s(t_bool,t))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => ![V_uu_3]: (![V_darku_u_shadowu_u_tupled, V_v]: s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))) = s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_4),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))) => ![V_uu_2]: (![V_darku_u_shadowu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_a),s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_bool))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))))) => ![V_uu_1]: (![V_darku_u_shadowu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),V_darku_u_shadowu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R)))) & ![V_L, V_c, V_lowers, V_uppers]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool)),V_uu_1))))))))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_bool,h4s_omegas_darku_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),h4s_omegas_darku_u_shadowu_u_tupled),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1)))))).
fof(ah4s_Omegas_nightmareu_u_impliesu_u_LHS, axiom, ![V_x, V_uppers, V_rs, V_lowers, V_c]: (p(s(t_bool,h4s_omegas_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_c),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))) => (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))))).
fof(ah4s_Omegas_darku_u_shadowu_u_FORALL, axiom, ![V_uppers, V_lowers]: (p(s(t_bool,h4s_omegas_darku_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) <=> ![V_c, V_d, V_L, V_R]: ((p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))))) & p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))))) => p(s(t_bool,h4s_integers_intu_u_ge(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_L))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_R))))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))).
fof(ah4s_Omegas_evalupperu_u_FORALL, axiom, ![V_x, V_uppers]: (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) <=> ![V_c, V_L]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_c),s(t_h4s_integers_int,V_L))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_L))))))).
fof(ah4s_Omegas_evalloweru_u_FORALL, axiom, ![V_x, V_lowers]: (p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) <=> ![V_d, V_R]: (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))) => p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_R),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_x))))))))).
fof(ah4s_Omegas_nightmareu_u_EXISTS, axiom, ![V_x, V_uppers, V_rs, V_lowers, V_c]: (p(s(t_bool,h4s_omegas_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_c),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))) <=> ?[V_i, V_d, V_R]: (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c)))))))) & (p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))) & (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & (p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_R),s(t_h4s_integers_int,V_i)))))))))).
fof(ch4s_Omegas_finalu_u_equivalence, conjecture, ![V_uu_0]: (![V_m, V_p]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_p))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_p))),s(t_h4s_nums_num,V_m))) => ![V_uppers, V_m, V_lowers]: ((p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_omegas_fstu_u_nzero),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & (p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),h4s_omegas_fstu_u_nzero),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),t_bool)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))))) => (?[V_x]: (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) <=> (p(s(t_bool,h4s_omegas_realu_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) & (p(s(t_bool,h4s_omegas_darku_u_shadow(s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))) | ?[V_x]: p(s(t_bool,h4s_omegas_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))))).
