%   ORIGINAL: h4/Omega/calculational__nightmare
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/LEFT__OR__EXISTS__THM: !Q P. (?x. P x) \/ Q <=> (?x. P x \/ Q)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__size__def_c1: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/list/list__size f a1))
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/integer/INT__MUL: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm: h4/Omega/nightmare__tupled__primitive__def: h4/Omega/nightmare__tupled = h4/relation/WFREC (h4/min/_40 (\R_27. h4/relation/WF R_27 /\ (!R d rs lowers uppers c x. R_27 (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers rs)))) (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers (h4/list/CONS (h4/pair/_2C d R) rs)))))))) (\nightmare__tupled a. h4/pair/pair__CASE a (\x v1. h4/pair/pair__CASE v1 (\c v3. h4/pair/pair__CASE v3 (\uppers v5. h4/pair/pair__CASE v5 (\lowers v7. h4/list/list__CASE v7 (h4/combin/I F) (\v8 rs. h4/pair/pair__CASE v8 (\d R. h4/combin/I ((?i. (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c))) /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) \/ nightmare__tupled (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers rs))))))))))))
% Assm: h4/Omega/nightmare__curried__def: !x4 x3 x2 x1 x. h4/Omega/nightmare x x1 x2 x3 x4 <=> h4/Omega/nightmare__tupled (h4/pair/_2C x (h4/pair/_2C x1 (h4/pair/_2C x2 (h4/pair/_2C x3 x4))))
% Assm: h4/Omega/calc__nightmare__tupled__primitive__def: h4/Omega/calc__nightmare__tupled = h4/relation/WFREC (h4/min/_40 (\R_27. h4/relation/WF R_27 /\ (!R d rs c x. R_27 (h4/pair/_2C x (h4/pair/_2C c rs)) (h4/pair/_2C x (h4/pair/_2C c (h4/list/CONS (h4/pair/_2C d R) rs)))))) (\calc__nightmare__tupled a. h4/pair/pair__CASE a (\x v1. h4/pair/pair__CASE v1 (\c v3. h4/list/list__CASE v3 (h4/combin/I F) (\v4 rs. h4/pair/pair__CASE v4 (\d R. h4/combin/I ((?i. (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c))) /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i) \/ calc__nightmare__tupled (h4/pair/_2C x (h4/pair/_2C c rs))))))))
% Assm: h4/Omega/calc__nightmare__curried__def: !x2 x1 x. h4/Omega/calc__nightmare x x1 x2 <=> h4/Omega/calc__nightmare__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs <=> h4/Omega/calc__nightmare x c rs /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_LEFTu_u_ORu_u_EXISTSu_u_THM]: !Q P. (?x. happ P x) \/ Q <=> (?x. happ P x \/ Q)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_sizeu_u_defu_c1]: !f a1 a0. h4/list/list__size f (h4/list/CONS a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/list/list__size f a1))
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_integers_INTu_u_MUL]: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Assm [h4s_Omegas_nightmareu_u_tupledu_u_primitiveu_u_def]: !_14. (!d nightmare__tupled x c uppers lowers rs R. ?v. (v <=> (?i. (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c))) /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers) \/ happ nightmare__tupled (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers rs))))) /\ (happ (happ (happ (happ (happ (happ (happ (happ _14 d) nightmare__tupled) x) c) uppers) lowers) rs) R <=> h4/combin/I v)) ==> (!_13. (!nightmare__tupled x c uppers lowers rs d. happ (happ (happ (happ (happ (happ (happ _13 nightmare__tupled) x) c) uppers) lowers) rs) d = happ (happ (happ (happ (happ (happ (happ _14 d) nightmare__tupled) x) c) uppers) lowers) rs) ==> (!_12. (!v8 nightmare__tupled x c uppers lowers rs. happ (happ (happ (happ (happ (happ (happ _12 v8) nightmare__tupled) x) c) uppers) lowers) rs <=> h4/pair/pair__CASE v8 (happ (happ (happ (happ (happ (happ _13 nightmare__tupled) x) c) uppers) lowers) rs)) ==> (!_11. (!nightmare__tupled x c uppers lowers v8. happ (happ (happ (happ (happ (happ _11 nightmare__tupled) x) c) uppers) lowers) v8 = happ (happ (happ (happ (happ (happ _12 v8) nightmare__tupled) x) c) uppers) lowers) ==> (!_10. (!nightmare__tupled x c uppers lowers v7. happ (happ (happ (happ (happ (happ _10 nightmare__tupled) x) c) uppers) lowers) v7 <=> h4/list/list__CASE v7 (h4/combin/I F) (happ (happ (happ (happ (happ _11 nightmare__tupled) x) c) uppers) lowers)) ==> (!_9. (!nightmare__tupled x c uppers lowers. happ (happ (happ (happ (happ _9 nightmare__tupled) x) c) uppers) lowers = happ (happ (happ (happ (happ _10 nightmare__tupled) x) c) uppers) lowers) ==> (!_8. (!nightmare__tupled x c uppers v5. happ (happ (happ (happ (happ _8 nightmare__tupled) x) c) uppers) v5 <=> h4/pair/pair__CASE v5 (happ (happ (happ (happ _9 nightmare__tupled) x) c) uppers)) ==> (!_7. (!nightmare__tupled x c uppers. happ (happ (happ (happ _7 nightmare__tupled) x) c) uppers = happ (happ (happ (happ _8 nightmare__tupled) x) c) uppers) ==> (!_6. (!nightmare__tupled x c v3. happ (happ (happ (happ _6 nightmare__tupled) x) c) v3 <=> h4/pair/pair__CASE v3 (happ (happ (happ _7 nightmare__tupled) x) c)) ==> (!_5. (!nightmare__tupled x c. happ (happ (happ _5 nightmare__tupled) x) c = happ (happ (happ _6 nightmare__tupled) x) c) ==> (!_4. (!nightmare__tupled x v1. happ (happ (happ _4 nightmare__tupled) x) v1 <=> h4/pair/pair__CASE v1 (happ (happ _5 nightmare__tupled) x)) ==> (!_3. (!nightmare__tupled x. happ (happ _3 nightmare__tupled) x = happ (happ _4 nightmare__tupled) x) ==> (!_2. (!nightmare__tupled a. happ (happ _2 nightmare__tupled) a <=> h4/pair/pair__CASE a (happ _3 nightmare__tupled)) ==> (!_1. (!nightmare__tupled. happ _1 nightmare__tupled = happ _2 nightmare__tupled) ==> (!_0. (!R_27. happ _0 R_27 <=> h4/relation/WF R_27 /\ (!R d rs lowers uppers c x. happ (happ R_27 (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers rs))))) (h4/pair/_2C x (h4/pair/_2C c (h4/pair/_2C uppers (h4/pair/_2C lowers (h4/list/CONS (h4/pair/_2C d R) rs))))))) ==> h4/Omega/nightmare__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))
% Assm [h4s_Omegas_nightmareu_u_curriedu_u_def]: !x4 x3 x2 x1 x. h4/Omega/nightmare x x1 x2 x3 x4 <=> happ h4/Omega/nightmare__tupled (h4/pair/_2C x (h4/pair/_2C x1 (h4/pair/_2C x2 (h4/pair/_2C x3 x4))))
% Assm [h4s_Omegas_calcu_u_nightmareu_u_tupledu_u_primitiveu_u_def]: !_10. (!d calc__nightmare__tupled x c rs R. ?v. (v <=> (?i. (h4/integer/int__le (h4/integer/int__of__num h4/num/0) i /\ h4/integer/int__le i (h4/integer/int__div (h4/integer/int__sub (h4/integer/int__sub (h4/integer/int__mul (h4/integer/int__of__num c) (h4/integer/int__of__num d)) (h4/integer/int__of__num c)) (h4/integer/int__of__num d)) (h4/integer/int__of__num c))) /\ h4/integer/int__mul (h4/integer/int__of__num d) x = h4/integer/int__add R i) \/ happ calc__nightmare__tupled (h4/pair/_2C x (h4/pair/_2C c rs))) /\ (happ (happ (happ (happ (happ (happ _10 d) calc__nightmare__tupled) x) c) rs) R <=> h4/combin/I v)) ==> (!_9. (!calc__nightmare__tupled x c rs d. happ (happ (happ (happ (happ _9 calc__nightmare__tupled) x) c) rs) d = happ (happ (happ (happ (happ _10 d) calc__nightmare__tupled) x) c) rs) ==> (!_8. (!v4 calc__nightmare__tupled x c rs. happ (happ (happ (happ (happ _8 v4) calc__nightmare__tupled) x) c) rs <=> h4/pair/pair__CASE v4 (happ (happ (happ (happ _9 calc__nightmare__tupled) x) c) rs)) ==> (!_7. (!calc__nightmare__tupled x c v4. happ (happ (happ (happ _7 calc__nightmare__tupled) x) c) v4 = happ (happ (happ (happ _8 v4) calc__nightmare__tupled) x) c) ==> (!_6. (!calc__nightmare__tupled x c v3. happ (happ (happ (happ _6 calc__nightmare__tupled) x) c) v3 <=> h4/list/list__CASE v3 (h4/combin/I F) (happ (happ (happ _7 calc__nightmare__tupled) x) c)) ==> (!_5. (!calc__nightmare__tupled x c. happ (happ (happ _5 calc__nightmare__tupled) x) c = happ (happ (happ _6 calc__nightmare__tupled) x) c) ==> (!_4. (!calc__nightmare__tupled x v1. happ (happ (happ _4 calc__nightmare__tupled) x) v1 <=> h4/pair/pair__CASE v1 (happ (happ _5 calc__nightmare__tupled) x)) ==> (!_3. (!calc__nightmare__tupled x. happ (happ _3 calc__nightmare__tupled) x = happ (happ _4 calc__nightmare__tupled) x) ==> (!_2. (!calc__nightmare__tupled a. happ (happ _2 calc__nightmare__tupled) a <=> h4/pair/pair__CASE a (happ _3 calc__nightmare__tupled)) ==> (!_1. (!calc__nightmare__tupled. happ _1 calc__nightmare__tupled = happ _2 calc__nightmare__tupled) ==> (!_0. (!R_27. happ _0 R_27 <=> h4/relation/WF R_27 /\ (!R d rs c x. happ (happ R_27 (h4/pair/_2C x (h4/pair/_2C c rs))) (h4/pair/_2C x (h4/pair/_2C c (h4/list/CONS (h4/pair/_2C d R) rs))))) ==> h4/Omega/calc__nightmare__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_Omegas_calcu_u_nightmareu_u_curriedu_u_def]: !x2 x1 x. h4/Omega/calc__nightmare x x1 x2 <=> happ h4/Omega/calc__nightmare__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !x uppers rs lowers c. h4/Omega/nightmare x c uppers lowers rs <=> h4/Omega/calc__nightmare x c rs /\ h4/Omega/evalupper x uppers /\ h4/Omega/evallower x lowers
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q19593,TV_Q19589]: ![V_f, V_g]: (![V_x]: s(TV_Q19589,happ(s(t_fun(TV_Q19593,TV_Q19589),V_f),s(TV_Q19593,V_x))) = s(TV_Q19589,happ(s(t_fun(TV_Q19593,TV_Q19589),V_g),s(TV_Q19593,V_x))) => s(t_fun(TV_Q19593,TV_Q19589),V_f) = s(t_fun(TV_Q19593,TV_Q19589),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_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_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))) <=> ?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) & ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_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_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(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,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_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_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_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_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_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_lists_list(TV_u_27a),V_a1)))))))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_integers_INTu_u_MUL, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_Omegas_nightmareu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_14]: (![V_d, V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers, V_rs, V_R]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (?[V_i]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))))))) & (s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_R),s(t_h4s_integers_int,V_i))) & (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))))) | p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_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_lowers),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_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_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_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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_14),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_integers_int,V_R))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_13]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers, 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_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_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_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_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_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_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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_13),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),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_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_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_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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_14),s(t_h4s_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_12]: (![V_v8, V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers, 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_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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_12),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v8))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v8),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_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_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_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_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_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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_13),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_11]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers, V_v8]: 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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_11),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v8))) = 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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_12),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),V_v8))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_10]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers, V_v7]: 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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_10),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_v7))) = 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_v7),s(t_bool,h4s_combins_i(s(t_bool,f))),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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_11),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))))) => ![V_uu_9]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_lowers]: 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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_9),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) = s(t_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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_10),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers))) => ![V_uu_8]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers, V_v5]: 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_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)),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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_8),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))),s(t_h4s_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_v5))) = 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_v5),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_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_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_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_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_9),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))))) => ![V_uu_7]: (![V_nightmareu_u_tupled, V_x, V_c, V_uppers]: 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_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)),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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_7),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))) = s(t_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_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)),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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_8),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers))) => ![V_uu_6]: (![V_nightmareu_u_tupled, V_x, V_c, V_v3]: 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_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_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_6),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_v3))) = 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_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_v3),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_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_nums_num,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_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_integers_int,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,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_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_7),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))))) => ![V_uu_5]: (![V_nightmareu_u_tupled, V_x, 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_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_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_5),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),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_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_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_6),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))) => ![V_uu_4]: (![V_nightmareu_u_tupled, V_x, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_4),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_v1))) = 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=> ![V_uu_3]: (![V_nightmareu_u_tupled, V_x]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_3),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_4),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_2]: (![V_nightmareu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_3),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))))) => ![V_uu_1]: (![V_nightmareu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled))) => ![V_uu_0]: (![V_Ru_27]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_Ru_27)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_Ru_27)))) & ![V_R, V_d, V_rs, V_lowers, V_uppers, V_c, V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_Ru_27),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_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_lowers),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nums_num,V_c),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_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_lowers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),h4s_lists_cons(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_nums_num,V_d),s(t_h4s_integers_int,V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_curriedu_u_def, axiom, ![V_x4, V_x3, V_x2, V_x1, V_x]: s(t_bool,h4s_omegas_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x3),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x4))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nightmareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_integers_int,V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_nums_num,V_x1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),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_x2),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_x3),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x4)))))))))))).
fof(ah4s_Omegas_calcu_u_nightmareu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_10]: (![V_d, V_calcu_u_nightmareu_u_tupled, V_x, V_c, V_rs, V_R]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (?[V_i]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_i)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_c))))))))) & s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_d))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_R),s(t_h4s_integers_int,V_i)))) | p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_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_h4s_integers_int,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_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_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))),s(t_h4s_integers_int,V_R))) = s(t_bool,h4s_combins_i(s(t_bool,V_v)))) => ![V_uu_9]: (![V_calcu_u_nightmareu_u_tupled, V_x, V_c, 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_nums_num,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_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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_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_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_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_pairs_prod(t_h4s_nums_num,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_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_nums_num,V_d))),s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))) => ![V_uu_8]: (![V_v4, V_calcu_u_nightmareu_u_tupled, V_x, V_c, 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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_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_nums_num,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_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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))) => ![V_uu_7]: (![V_calcu_u_nightmareu_u_tupled, V_x, V_c, 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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))) => ![V_uu_6]: (![V_calcu_u_nightmareu_u_tupled, V_x, V_c, 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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_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,f))),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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))))) => ![V_uu_5]: (![V_calcu_u_nightmareu_u_tupled, V_x, V_c]: 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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))) = 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_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,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_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_nums_num,V_c))) => ![V_uu_4]: (![V_calcu_u_nightmareu_u_tupled, V_x, V_v1]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))),s(t_h4s_pairs_prod(t_h4s_nums_num,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_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int))),V_v1),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_bool)),happ(s(t_fun(t_h4s_integers_int,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_bool))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))))) => ![V_uu_3]: (![V_calcu_u_nightmareu_u_tupled, V_x]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_integers_int,V_x))) => ![V_uu_2]: (![V_calcu_u_nightmareu_u_tupled, V_a]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))))) => ![V_uu_1]: (![V_calcu_u_nightmareu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),V_calcu_u_nightmareu_u_tupled))) => ![V_uu_0]: (![V_Ru_27]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_c, V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs))))))),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_calcu_u_nightmareu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool)),V_uu_1))))))))))))))).
fof(ah4s_Omegas_calcu_u_nightmareu_u_curriedu_u_def, axiom, ![V_x2, V_x1, V_x]: s(t_bool,h4s_omegas_calcu_u_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,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_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)))),t_bool),h4s_omegas_calcu_u_nightmareu_u_tupled),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,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_x1),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_x2)))))))).
fof(ch4s_Omegas_calculationalu_u_nightmare, conjecture, ![V_x, V_uppers, V_rs, V_lowers, V_c]: (p(s(t_bool,h4s_omegas_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_c),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))) <=> (p(s(t_bool,h4s_omegas_calcu_u_nightmare(s(t_h4s_integers_int,V_x),s(t_h4s_nums_num,V_c),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_rs)))) & (p(s(t_bool,h4s_omegas_evalupper(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_uppers)))) & p(s(t_bool,h4s_omegas_evallower(s(t_h4s_integers_int,V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_integers_int)),V_lowers)))))))).
