%   ORIGINAL: h4/Omega/dark__shadow__row__def_c0
% 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/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/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% Assm: h4/Omega/rshadow__row__def_c0: !uppery upperc. h4/Omega/rshadow__row (h4/pair/_2C upperc uppery) h4/list/NIL <=> T
% Assm: h4/Omega/rshadow__row__tupled__primitive__def: h4/Omega/rshadow__row__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!lowery lowerc rs uppery upperc. R (h4/pair/_2C (h4/pair/_2C upperc uppery) rs) (h4/pair/_2C (h4/pair/_2C upperc uppery) (h4/list/CONS (h4/pair/_2C lowerc lowery) rs))))) (\rshadow__row__tupled a. h4/pair/pair__CASE a (\v v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 rs. h4/pair/pair__CASE v2 (\lowerc lowery. h4/pair/pair__CASE v (\upperc uppery. h4/combin/I (h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num upperc) lowery) (h4/integer/int__mul (h4/integer/int__of__num lowerc) uppery) /\ rshadow__row__tupled (h4/pair/_2C (h4/pair/_2C upperc uppery) rs)))))))
% Assm: h4/Omega/dark__shadow__cond__row__def_c0: !c L. h4/Omega/dark__shadow__cond__row (h4/pair/_2C c L) h4/list/NIL <=> T
% 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/evallower__def_c0: !x. h4/Omega/evallower x h4/list/NIL <=> T
% Assm: h4/Omega/evallower__tupled__primitive__def: h4/Omega/evallower__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y c cs x. R (h4/pair/_2C x cs) (h4/pair/_2C x (h4/list/CONS (h4/pair/_2C c y) cs))))) (\evallower__tupled a. h4/pair/pair__CASE a (\x v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 cs. h4/pair/pair__CASE v2 (\c y. h4/combin/I (h4/integer/int__le y (h4/integer/int__mul (h4/integer/int__of__num c) x) /\ evallower__tupled (h4/pair/_2C x cs))))))
% Assm: h4/Omega/evalupper__def_c0: !x. h4/Omega/evalupper x h4/list/NIL <=> T
% Assm: h4/Omega/evalupper__tupled__primitive__def: h4/Omega/evalupper__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y c cs x. R (h4/pair/_2C x cs) (h4/pair/_2C x (h4/list/CONS (h4/pair/_2C c y) cs))))) (\evalupper__tupled a. h4/pair/pair__CASE a (\x v1. h4/list/list__CASE v1 (h4/combin/I T) (\v2 cs. h4/pair/pair__CASE v2 (\c y. h4/combin/I (h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) x) y /\ evalupper__tupled (h4/pair/_2C x cs))))))
% 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__def_c0: !lowers. h4/Omega/dark__shadow__condition h4/list/NIL lowers <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/TRUTH: T
% Assm: h4/Omega/real__shadow__def_c0: !lowers. h4/Omega/real__shadow h4/list/NIL lowers <=> T
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% 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/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% 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__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% 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/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/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% 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/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/integer/INT__DIVIDES__REDUCE_c3: !p. h4/integer/int__divides p (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/list/EVERYi__DEF_c0: !P. h4/list/EVERYi P h4/list/NIL <=> T
% Assm: h4/rich__list/IS__SUBLIST0_c0: !l. h4/rich__list/IS__SUBLIST l h4/list/NIL <=> T
% Assm: h4/rich__list/IS__SUFFIX0_c0: !l. h4/rich__list/IS__SUFFIX l h4/list/NIL <=> T
% Assm: h4/Omega/rshadow__row__curried__def: !x1 x. h4/Omega/rshadow__row x x1 <=> h4/Omega/rshadow__row__tupled (h4/pair/_2C x x1)
% 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/evallower__curried__def: !x1 x. h4/Omega/evallower x x1 <=> h4/Omega/evallower__tupled (h4/pair/_2C x x1)
% Assm: h4/Omega/evalupper__curried__def: !x1 x. h4/Omega/evalupper x x1 <=> h4/Omega/evalupper__tupled (h4/pair/_2C x x1)
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/list/NULL__DEF_c1: !t h. h4/list/NULL (h4/list/CONS h t) <=> F
% Assm: h4/list/NULL__DEF_c0: h4/list/NULL h4/list/NIL <=> T
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/integer/INT__EQ__CALCULATE_c0: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm: h4/integer/INT__MOD__REDUCE_c3: !n m. h4/integer/int__mod (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n))) = h4/integer/int__of__num (h4/arithmetic/MOD (h4/arithmetic/NUMERAL m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm: h4/integer/INT__DIVIDES__NEG_c0: !q p. h4/integer/int__divides p (h4/integer/int__neg q) <=> h4/integer/int__divides p q
% Assm: h4/integer/INT__DIVIDES__MOD0: !q p. h4/integer/int__divides p q <=> h4/integer/int__mod q p = h4/integer/int__of__num h4/num/0 /\ ~(p = h4/integer/int__of__num h4/num/0) \/ p = h4/integer/int__of__num h4/num/0 /\ q = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__DIVIDES__NEG_c1: !q p. h4/integer/int__divides (h4/integer/int__neg p) q <=> h4/integer/int__divides p q
% Assm: h4/integer/INT__MOD0: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num h4/num/0) p = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__MOD__REDUCE_c2: !n m. h4/integer/int__mod (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) = h4/integer/int__of__num (h4/arithmetic/MOD (h4/arithmetic/NUMERAL m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c3: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/arithmetic/BIT20: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm: h4/arithmetic/SUC__NOT: !n. ~(h4/num/0 = h4/num/SUC n)
% Assm: h4/arithmetic/BIT10: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/list/TL0: !t h. h4/list/TL (h4/list/CONS h t) = t
% Assm: h4/list/HD0: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~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/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/rich__list/NOT__NULL__SNOC: !x l. ~h4/list/NULL (h4/list/SNOC x l)
% Assm: h4/list/SNOC__Axiom: !f e. ?fn. fn h4/list/NIL = e /\ (!x l. fn (h4/list/SNOC x l) = f x l (fn l))
% Assm: h4/list/FRONT__SNOC: !x l. h4/list/FRONT (h4/list/SNOC x l) = l
% Assm: h4/list/LAST__SNOC: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Goal: !c L. h4/Omega/dark__shadow__row c L h4/list/NIL <=> T
%   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_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_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (happ (happ h4/list/CONS a0) a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_Omegas_rshadowu_u_rowu_u_defu_c0]: !uppery upperc. h4/Omega/rshadow__row (h4/pair/_2C upperc uppery) h4/list/NIL <=> T
% Assm [h4s_Omegas_rshadowu_u_rowu_u_tupledu_u_primitiveu_u_def]: !_10. (!lowery lowerc rshadow__row__tupled upperc rs uppery. ?v. (v <=> h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num upperc) lowery) (h4/integer/int__mul (h4/integer/int__of__num lowerc) uppery) /\ happ rshadow__row__tupled (h4/pair/_2C (h4/pair/_2C upperc uppery) rs)) /\ (happ (happ (happ (happ (happ (happ _10 lowery) lowerc) rshadow__row__tupled) upperc) rs) uppery <=> h4/combin/I v)) ==> (!_9. (!lowery lowerc rshadow__row__tupled rs upperc. happ (happ (happ (happ (happ _9 lowery) lowerc) rshadow__row__tupled) rs) upperc = happ (happ (happ (happ (happ _10 lowery) lowerc) rshadow__row__tupled) upperc) rs) ==> (!_8. (!v lowerc rshadow__row__tupled rs lowery. happ (happ (happ (happ (happ _8 v) lowerc) rshadow__row__tupled) rs) lowery <=> h4/pair/pair__CASE v (happ (happ (happ (happ _9 lowery) lowerc) rshadow__row__tupled) rs)) ==> (!_7. (!v rshadow__row__tupled rs lowerc. happ (happ (happ (happ _7 v) rshadow__row__tupled) rs) lowerc = happ (happ (happ (happ _8 v) lowerc) rshadow__row__tupled) rs) ==> (!_6. (!v2 v rshadow__row__tupled rs. happ (happ (happ (happ _6 v2) v) rshadow__row__tupled) rs <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 v) rshadow__row__tupled) rs)) ==> (!_5. (!v rshadow__row__tupled v2. happ (happ (happ _5 v) rshadow__row__tupled) v2 = happ (happ (happ _6 v2) v) rshadow__row__tupled) ==> (!_4. (!v rshadow__row__tupled v1. happ (happ (happ _4 v) rshadow__row__tupled) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 v) rshadow__row__tupled)) ==> (!_3. (!rshadow__row__tupled v. happ (happ _3 rshadow__row__tupled) v = happ (happ _4 v) rshadow__row__tupled) ==> (!_2. (!rshadow__row__tupled a. happ (happ _2 rshadow__row__tupled) a <=> h4/pair/pair__CASE a (happ _3 rshadow__row__tupled)) ==> (!_1. (!rshadow__row__tupled. happ _1 rshadow__row__tupled = happ _2 rshadow__row__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!lowery lowerc rs uppery upperc. happ (happ R (h4/pair/_2C (h4/pair/_2C upperc uppery) rs)) (h4/pair/_2C (h4/pair/_2C upperc uppery) (happ (happ h4/list/CONS (h4/pair/_2C lowerc lowery)) rs)))) ==> h4/Omega/rshadow__row__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_Omegas_darku_u_shadowu_u_condu_u_rowu_u_defu_c0]: !c L. h4/Omega/dark__shadow__cond__row (h4/pair/_2C c L) h4/list/NIL <=> T
% 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) (happ (happ 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_evalloweru_u_defu_c0]: !x. h4/Omega/evallower x h4/list/NIL <=> T
% Assm [h4s_Omegas_evalloweru_u_tupledu_u_primitiveu_u_def]: !_8. (!c evallower__tupled x cs y. ?v. (v <=> h4/integer/int__le y (h4/integer/int__mul (h4/integer/int__of__num c) x) /\ happ evallower__tupled (h4/pair/_2C x cs)) /\ (happ (happ (happ (happ (happ _8 c) evallower__tupled) x) cs) y <=> h4/combin/I v)) ==> (!_7. (!evallower__tupled x cs c. happ (happ (happ (happ _7 evallower__tupled) x) cs) c = happ (happ (happ (happ _8 c) evallower__tupled) x) cs) ==> (!_6. (!v2 evallower__tupled x cs. happ (happ (happ (happ _6 v2) evallower__tupled) x) cs <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 evallower__tupled) x) cs)) ==> (!_5. (!evallower__tupled x v2. happ (happ (happ _5 evallower__tupled) x) v2 = happ (happ (happ _6 v2) evallower__tupled) x) ==> (!_4. (!evallower__tupled x v1. happ (happ (happ _4 evallower__tupled) x) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 evallower__tupled) x)) ==> (!_3. (!evallower__tupled x. happ (happ _3 evallower__tupled) x = happ (happ _4 evallower__tupled) x) ==> (!_2. (!evallower__tupled a. happ (happ _2 evallower__tupled) a <=> h4/pair/pair__CASE a (happ _3 evallower__tupled)) ==> (!_1. (!evallower__tupled. happ _1 evallower__tupled = happ _2 evallower__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y c cs x. happ (happ R (h4/pair/_2C x cs)) (h4/pair/_2C x (happ (happ h4/list/CONS (h4/pair/_2C c y)) cs)))) ==> h4/Omega/evallower__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_Omegas_evalupperu_u_defu_c0]: !x. h4/Omega/evalupper x h4/list/NIL <=> T
% Assm [h4s_Omegas_evalupperu_u_tupledu_u_primitiveu_u_def]: !_8. (!c evalupper__tupled x cs y. ?v. (v <=> h4/integer/int__le (h4/integer/int__mul (h4/integer/int__of__num c) x) y /\ happ evalupper__tupled (h4/pair/_2C x cs)) /\ (happ (happ (happ (happ (happ _8 c) evalupper__tupled) x) cs) y <=> h4/combin/I v)) ==> (!_7. (!evalupper__tupled x cs c. happ (happ (happ (happ _7 evalupper__tupled) x) cs) c = happ (happ (happ (happ _8 c) evalupper__tupled) x) cs) ==> (!_6. (!v2 evalupper__tupled x cs. happ (happ (happ (happ _6 v2) evalupper__tupled) x) cs <=> h4/pair/pair__CASE v2 (happ (happ (happ _7 evalupper__tupled) x) cs)) ==> (!_5. (!evalupper__tupled x v2. happ (happ (happ _5 evalupper__tupled) x) v2 = happ (happ (happ _6 v2) evalupper__tupled) x) ==> (!_4. (!evalupper__tupled x v1. happ (happ (happ _4 evalupper__tupled) x) v1 <=> h4/list/list__CASE v1 (h4/combin/I T) (happ (happ _5 evalupper__tupled) x)) ==> (!_3. (!evalupper__tupled x. happ (happ _3 evalupper__tupled) x = happ (happ _4 evalupper__tupled) x) ==> (!_2. (!evalupper__tupled a. happ (happ _2 evalupper__tupled) a <=> h4/pair/pair__CASE a (happ _3 evalupper__tupled)) ==> (!_1. (!evalupper__tupled. happ _1 evalupper__tupled = happ _2 evalupper__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y c cs x. happ (happ R (h4/pair/_2C x cs)) (h4/pair/_2C x (happ (happ h4/list/CONS (h4/pair/_2C c y)) cs)))) ==> h4/Omega/evalupper__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% 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 (happ (happ 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_defu_c0]: !lowers. h4/Omega/dark__shadow__condition h4/list/NIL lowers <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_Omegas_realu_u_shadowu_u_defu_c0]: !lowers. h4/Omega/real__shadow h4/list/NIL lowers <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% 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 (happ (happ 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_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% 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_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_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (happ (happ h4/list/CONS a0) a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = 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_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_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_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_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% 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_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = 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_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (happ (happ 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_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_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_integers_INTu_u_DIVIDESu_u_REDUCEu_c3]: !p. h4/integer/int__divides p (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_lists_EVERYiu_u_DEFu_c0]: !P. h4/list/EVERYi P h4/list/NIL <=> T
% Assm [h4s_richu_u_lists_ISu_u_SUBLIST0u_c0]: !l. h4/rich__list/IS__SUBLIST l h4/list/NIL <=> T
% Assm [h4s_richu_u_lists_ISu_u_SUFFIX0u_c0]: !l. h4/rich__list/IS__SUFFIX l h4/list/NIL <=> T
% Assm [h4s_Omegas_rshadowu_u_rowu_u_curriedu_u_def]: !x1 x. h4/Omega/rshadow__row x x1 <=> happ h4/Omega/rshadow__row__tupled (h4/pair/_2C x x1)
% 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_evalloweru_u_curriedu_u_def]: !x1 x. h4/Omega/evallower x x1 <=> happ h4/Omega/evallower__tupled (h4/pair/_2C x x1)
% Assm [h4s_Omegas_evalupperu_u_curriedu_u_def]: !x1 x. h4/Omega/evalupper x x1 <=> happ h4/Omega/evalupper__tupled (h4/pair/_2C x x1)
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_lists_NULLu_u_DEFu_c1]: !t h. h4/list/NULL (happ (happ h4/list/CONS h) t) <=> F
% Assm [h4s_lists_NULLu_u_DEFu_c0]: h4/list/NULL h4/list/NIL <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_integers_INTu_u_EQu_u_CALCULATEu_c0]: !n m. h4/integer/int__of__num m = h4/integer/int__of__num n <=> m = n
% Assm [h4s_integers_INTu_u_MODu_u_REDUCEu_c3]: !n m. h4/integer/int__mod (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n))) = h4/integer/int__of__num (h4/arithmetic/MOD (h4/arithmetic/NUMERAL m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))
% Assm [h4s_integers_INTu_u_DIVIDESu_u_NEGu_c0]: !q p. h4/integer/int__divides p (h4/integer/int__neg q) <=> h4/integer/int__divides p q
% Assm [h4s_integers_INTu_u_DIVIDESu_u_MOD0]: !q p. h4/integer/int__divides p q <=> h4/integer/int__mod q p = h4/integer/int__of__num h4/num/0 /\ ~(p = h4/integer/int__of__num h4/num/0) \/ p = h4/integer/int__of__num h4/num/0 /\ q = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_DIVIDESu_u_NEGu_c1]: !q p. h4/integer/int__divides (h4/integer/int__neg p) q <=> h4/integer/int__divides p q
% Assm [h4s_integers_INTu_u_MOD0]: !p. ~(p = h4/integer/int__of__num h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num h4/num/0) p = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_MODu_u_REDUCEu_c2]: !n m. h4/integer/int__mod (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) = h4/integer/int__of__num (h4/arithmetic/MOD (h4/arithmetic/NUMERAL m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c3]: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_arithmetics_BIT20]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm [h4s_arithmetics_SUCu_u_NOT]: !n. ~(h4/num/0 = h4/num/SUC n)
% Assm [h4s_arithmetics_BIT10]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_lists_TL0]: !t h. h4/list/TL (happ (happ h4/list/CONS h) t) = t
% Assm [h4s_lists_HD0]: !t h. h4/list/HD (happ (happ h4/list/CONS h) t) = h
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_richu_u_lists_NOTu_u_NULLu_u_SNOC]: !x l. ~h4/list/NULL (h4/list/SNOC x l)
% Assm [h4s_lists_SNOCu_u_Axiom]: !f e. ?fn. happ fn h4/list/NIL = e /\ (!x l. happ fn (h4/list/SNOC x l) = happ (happ (happ f x) l) (happ fn l))
% Assm [h4s_lists_FRONTu_u_SNOC]: !x l. h4/list/FRONT (h4/list/SNOC x l) = l
% Assm [h4s_lists_LASTu_u_SNOC]: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Goal: !c L. h4/Omega/dark__shadow__row c L h4/list/NIL <=> T
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_Q1093881,TV_Q1093877]: ![V_f, V_g]: (![V_x]: s(TV_Q1093877,happ(s(t_fun(TV_Q1093881,TV_Q1093877),V_f),s(TV_Q1093881,V_x))) = s(TV_Q1093877,happ(s(t_fun(TV_Q1093881,TV_Q1093877),V_g),s(TV_Q1093881,V_x))) => s(t_fun(TV_Q1093881,TV_Q1093877),V_f) = s(t_fun(TV_Q1093881,TV_Q1093877),V_g))).
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_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_Omegas_rshadowu_u_rowu_u_defu_c0, axiom, ![V_uppery, V_upperc]: s(t_bool,h4s_omegas_rshadowu_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_upperc),s(t_h4s_integers_int,V_uppery))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_Omegas_rshadowu_u_rowu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_10]: (![V_lowery, V_lowerc, V_rshadowu_u_rowu_u_tupled, V_upperc, V_rs, V_uppery]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (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_upperc))),s(t_h4s_integers_int,V_lowery))),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_lowerc))),s(t_h4s_integers_int,V_uppery)))))) & 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_rshadowu_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_upperc),s(t_h4s_integers_int,V_uppery))),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_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_lowery))),s(t_h4s_nums_num,V_lowerc))),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_rshadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_upperc))),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_uppery))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_9]: (![V_lowery, V_lowerc, V_rshadowu_u_rowu_u_tupled, V_rs, V_upperc]: 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_lowery))),s(t_h4s_nums_num,V_lowerc))),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_rshadowu_u_rowu_u_tupled))),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_upperc))) = 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_lowery))),s(t_h4s_nums_num,V_lowerc))),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_rshadowu_u_rowu_u_tupled))),s(t_h4s_nums_num,V_upperc))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_8]: (![V_v, V_lowerc, V_rshadowu_u_rowu_u_tupled, V_rs, V_lowery]: 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_lowerc))),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_rshadowu_u_rowu_u_tupled))),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_lowery))) = 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_lowery))),s(t_h4s_nums_num,V_lowerc))),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_rshadowu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_7]: (![V_v, V_rshadowu_u_rowu_u_tupled, V_rs, V_lowerc]: 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_rshadowu_u_rowu_u_tupled))),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_lowerc))) = 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_lowerc))),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_rshadowu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_6]: (![V_v2, V_v, V_rshadowu_u_rowu_u_tupled, 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_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_rshadowu_u_rowu_u_tupled))),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_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_rshadowu_u_rowu_u_tupled))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_5]: (![V_v, V_rshadowu_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_rshadowu_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_rshadowu_u_rowu_u_tupled))) => ![V_uu_4]: (![V_v, V_rshadowu_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_rshadowu_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_rshadowu_u_rowu_u_tupled))))) => ![V_uu_3]: (![V_rshadowu_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_rshadowu_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_rshadowu_u_rowu_u_tupled))) => ![V_uu_2]: (![V_rshadowu_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_rshadowu_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_rshadowu_u_rowu_u_tupled))))) => ![V_uu_1]: (![V_rshadowu_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_rshadowu_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_rshadowu_u_rowu_u_tupled))) => ![V_uu_0]: (![V_R]: (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_R)))) <=> (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_R)))) & ![V_lowery, V_lowerc, V_rs, V_uppery, V_upperc]: 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_R),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_upperc),s(t_h4s_integers_int,V_uppery))),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_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_upperc),s(t_h4s_integers_int,V_uppery))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),happ(s(t_fun(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))),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_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_lowerc),s(t_h4s_integers_int,V_lowery))))),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_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_rshadowu_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_defu_c0, axiom, ![V_c, V_L]: 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)),h4s_lists_nil))) = s(t_bool,t)).
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)),happ(s(t_fun(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))),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_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_evalloweru_u_defu_c0, axiom, ![V_x]: 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)),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_Omegas_evalloweru_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_c, V_evalloweru_u_tupled, V_x, V_cs, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_integers_intu_u_le(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_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,V_x)))))) & p(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),V_evalloweru_u_tupled),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs)))))))) & 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_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),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_8),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),V_evalloweru_u_tupled))),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_cs))),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_evalloweru_u_tupled, V_x, V_cs, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_7),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),V_evalloweru_u_tupled))),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_cs))),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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_8),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),V_evalloweru_u_tupled))),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_cs))) => ![V_uu_6]: (![V_v2, V_evalloweru_u_tupled, V_x, V_cs]: 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_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),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),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),V_evalloweru_u_tupled))),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_cs))) = 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_7),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),V_evalloweru_u_tupled))),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_cs))))) => ![V_uu_5]: (![V_evalloweru_u_tupled, V_x, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_5),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),V_evalloweru_u_tupled))),s(t_h4s_integers_int,V_x))),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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),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),V_evalloweru_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_4]: (![V_evalloweru_u_tupled, V_x, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_4),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),V_evalloweru_u_tupled))),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_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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_5),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),V_evalloweru_u_tupled))),s(t_h4s_integers_int,V_x))))) => ![V_uu_3]: (![V_evalloweru_u_tupled, V_x]: 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_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),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_3),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),V_evalloweru_u_tupled))),s(t_h4s_integers_int,V_x))) = 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_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),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_4),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),V_evalloweru_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_2]: (![V_evalloweru_u_tupled, V_a]: 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_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),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_2),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),V_evalloweru_u_tupled))),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_a))) = 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_a),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_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),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_3),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),V_evalloweru_u_tupled))))) => ![V_uu_1]: (![V_evalloweru_u_tupled]: 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_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),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_1),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),V_evalloweru_u_tupled))) = 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_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),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_2),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),V_evalloweru_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(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_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)),t_bool),V_uu_0),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_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_R)))) <=> (p(s(t_bool,h4s_relations_wf(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_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_R)))) & ![V_y, V_c, V_cs, V_x]: p(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_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_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_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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs))))),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),happ(s(t_fun(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))),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_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_y))))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs)))))))))) => 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),h4s_omegas_evalloweru_u_tupled) = 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),h4s_relations_wfrec(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_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)),h4s_mins_u_40(s(t_fun(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_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)),t_bool),V_uu_0))),s(t_fun(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),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_1))))))))))))).
fof(ah4s_Omegas_evalupperu_u_defu_c0, axiom, ![V_x]: 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)),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_Omegas_evalupperu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_c, V_evalupperu_u_tupled, V_x, V_cs, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (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_y)))) & p(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),V_evalupperu_u_tupled),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs)))))))) & 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_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),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_8),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),V_evalupperu_u_tupled))),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_cs))),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_7]: (![V_evalupperu_u_tupled, V_x, V_cs, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_7),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),V_evalupperu_u_tupled))),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_cs))),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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_8),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),V_evalupperu_u_tupled))),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_cs))) => ![V_uu_6]: (![V_v2, V_evalupperu_u_tupled, V_x, V_cs]: 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_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),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),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),V_evalupperu_u_tupled))),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_cs))) = 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_7),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),V_evalupperu_u_tupled))),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_cs))))) => ![V_uu_5]: (![V_evalupperu_u_tupled, V_x, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_5),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),V_evalupperu_u_tupled))),s(t_h4s_integers_int,V_x))),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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v2))),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),V_evalupperu_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_4]: (![V_evalupperu_u_tupled, V_x, 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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_4),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),V_evalupperu_u_tupled))),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_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_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_integers_int,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),t_bool),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_5),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),V_evalupperu_u_tupled))),s(t_h4s_integers_int,V_x))))) => ![V_uu_3]: (![V_evalupperu_u_tupled, V_x]: 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_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),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_3),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),V_evalupperu_u_tupled))),s(t_h4s_integers_int,V_x))) = 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_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),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_4),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),V_evalupperu_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_2]: (![V_evalupperu_u_tupled, V_a]: 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_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),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_2),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),V_evalupperu_u_tupled))),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_a))) = 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_a),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_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),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_3),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),V_evalupperu_u_tupled))))) => ![V_uu_1]: (![V_evalupperu_u_tupled]: 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_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),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_1),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),V_evalupperu_u_tupled))) = 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_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),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_2),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),V_evalupperu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(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_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)),t_bool),V_uu_0),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_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_R)))) <=> (p(s(t_bool,h4s_relations_wf(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_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_R)))) & ![V_y, V_c, V_cs, V_x]: p(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_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_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_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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs))))),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),happ(s(t_fun(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))),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_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_y))))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_cs)))))))))) => 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),h4s_omegas_evalupperu_u_tupled) = 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),h4s_relations_wfrec(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_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)),h4s_mins_u_40(s(t_fun(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_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)),t_bool),V_uu_0))),s(t_fun(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),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_1))))))))))))).
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)),happ(s(t_fun(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))),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_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_defu_c0, axiom, ![V_lowers]: 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)),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) = s(t_bool,t)).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_Omegas_realu_u_shadowu_u_defu_c0, axiom, ![V_lowers]: 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)),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) = s(t_bool,t)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_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_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)),happ(s(t_fun(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))),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_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_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_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_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_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_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_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_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_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),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_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_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_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_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_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_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_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_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_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_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_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_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),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_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_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_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_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_pairs_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_integers_INTu_u_DIVIDESu_u_REDUCEu_c3, axiom, ![V_p]: s(t_bool,h4s_integers_intu_u_divides(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_bool,t)).
fof(ah4s_lists_EVERYiu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_everyi(s(t_fun(t_h4s_nums_num,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_richu_u_lists_ISu_u_SUBLIST0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_bool,h4s_richu_u_lists_isu_u_sublist(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_richu_u_lists_ISu_u_SUFFIX0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_bool,h4s_richu_u_lists_isu_u_suffix(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_Omegas_rshadowu_u_rowu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_bool,h4s_omegas_rshadowu_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_rshadowu_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_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_evalloweru_u_curriedu_u_def, axiom, ![V_x1, V_x]: 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_x1))) = 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),h4s_omegas_evalloweru_u_tupled),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1)))))).
fof(ah4s_Omegas_evalupperu_u_curriedu_u_def, axiom, ![V_x1, V_x]: 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_x1))) = 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),h4s_omegas_evalupperu_u_tupled),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_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x1)))))).
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_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_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_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_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_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_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_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ORu_u_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_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_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_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_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_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_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_lists_NULLu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_bool,f)).
fof(ah4s_lists_NULLu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),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_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(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_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, 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_integers_INTu_u_EQu_u_CALCULATEu_c0, 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_MODu_u_REDUCEu_c3, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mod(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,V_m))))),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_bit2(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_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_NEGu_c0, axiom, ![V_q, V_p]: s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_q))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_MOD0, axiom, ![V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) <=> ((s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,V_q),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,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,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,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_DIVIDESu_u_NEGu_c1, axiom, ![V_q, V_p]: s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_p))),s(t_h4s_integers_int,V_q))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))).
fof(ah4s_integers_INTu_u_MOD0, 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_mod(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))) = 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_REDUCEu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mod(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,V_m))))),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,V_n))))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))))))).
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_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_arithmetics_ADDu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c3, 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,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
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_arithmetics_BIT20, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_arithmetics_SUCu_u_NOT, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_BIT10, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_lists_TL0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),V_t)).
fof(ah4s_lists_HD0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(TV_u_27a,V_h)).
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_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),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_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_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_richu_u_lists_NOTu_u_NULLu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l)))))))).
fof(ah4s_lists_SNOCu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_e]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e) & ![V_x, V_l]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_lists_FRONTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_LASTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,V_x)).
fof(ch4s_Omegas_darku_u_shadowu_u_rowu_u_defu_c0, conjecture, ![V_c, V_L]: 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)),h4s_lists_nil))) = s(t_bool,t)).
