%   ORIGINAL: h4/string/EXPLODE__ONTO
% 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/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% Assm: h4/string/EXPLODE__def_c1: !s c. h4/string/EXPLODE (h4/list/CONS c s) = h4/list/CONS c (h4/string/EXPLODE s)
% Assm: h4/string/IMPLODE__EXPLODE__I_c0: !s. h4/string/EXPLODE s = s
% Assm: h4/string/IMPLODE__EXPLODE: !s. h4/string/IMPLODE (h4/string/EXPLODE s) = s
% Assm: h4/string/EXPLODE__def_c0: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/string/IMPLODE__def_c1: !cs c. h4/string/IMPLODE (h4/list/CONS c cs) = h4/list/CONS c (h4/string/IMPLODE cs)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/string/IMPLODE__def_c0: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/string/EXPLODE__IMPLODE: !cs. h4/string/EXPLODE (h4/string/IMPLODE cs) = cs
% Assm: h4/string/FIELDS__curried__def: !x1 x. h4/string/FIELDS x x1 = h4/string/FIELDS__tupled (h4/pair/_2C x x1)
% Assm: h4/string/FIELDS__tupled__primitive__def: h4/string/FIELDS__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))))) (\FIELDS__tupled a. h4/pair/pair__CASE a (\P v1. h4/list/list__CASE v1 (h4/combin/I (h4/list/CONS h4/list/NIL h4/list/NIL)) (\h t. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (FIELDS__tupled (h4/pair/_2C P (h4/list/TL r))))))) (h4/rich__list/SPLITP P (h4/list/CONS h t))))))
% Assm: h4/string/TOKENS__tupled__primitive__def: h4/string/TOKENS__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> R (h4/pair/_2C P (h4/list/TL r)) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> R (h4/pair/_2C P r) (h4/pair/_2C P (h4/list/CONS h t))))) (\TOKENS__tupled a. h4/pair/pair__CASE a (\P v1. h4/list/list__CASE v1 (h4/combin/I h4/list/NIL) (\h t. h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (TOKENS__tupled (h4/pair/_2C P (h4/list/TL r))) (h4/list/CONS l (TOKENS__tupled (h4/pair/_2C P r))))) (h4/rich__list/SPLITP P (h4/list/CONS h t))))))
% Assm: h4/string/TOKENS__curried__def: !x1 x. h4/string/TOKENS x x1 = h4/string/TOKENS__tupled (h4/pair/_2C x x1)
% Assm: h4/string/TOCHAR__primitive__def: h4/string/TOCHAR = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\TOCHAR a. h4/list/list__CASE a h4/bool/ARB (\c v1. h4/list/list__CASE v1 (h4/combin/I c) (\v2 v3. h4/bool/ARB)))
% Assm: h4/string/IMPLODE__EXPLODE__I_c1: !s. h4/string/IMPLODE s = s
% Assm: h4/string/FIELDS__def_c1: !t h P. h4/string/FIELDS P (h4/list/CONS h t) = h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (h4/string/FIELDS P (h4/list/TL r))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (h4/string/FIELDS P (h4/list/TL r)))))) (h4/rich__list/SPLITP P (h4/list/CONS h t))
% Assm: h4/string/FIELDS__ind: !P_27. (!P. P_27 P h4/list/NIL) /\ (!P h t. (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> P_27 P (h4/list/TL r)) /\ (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> P_27 P (h4/list/TL r)) ==> P_27 P (h4/list/CONS h t)) ==> (!v v1. P_27 v v1)
% Assm: h4/string/TRANSLATE__def: !s f. h4/string/TRANSLATE f s = h4/list/FLAT (h4/list/MAP f s)
% Assm: h4/string/TOKENS__ind: !P_27. (!P. P_27 P h4/list/NIL) /\ (!P h t. (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> P_27 P (h4/list/TL r)) /\ (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> P_27 P r) ==> P_27 P (h4/list/CONS h t)) ==> (!v v1. P_27 v v1)
% Assm: h4/string/TOKENS__def_c1: !t h P. h4/string/TOKENS P (h4/list/CONS h t) = h4/bool/LET (h4/pair/UNCURRY (\l r. h4/bool/COND (h4/list/NULL l) (h4/string/TOKENS P (h4/list/TL r)) (h4/list/CONS l (h4/string/TOKENS P r)))) (h4/rich__list/SPLITP P (h4/list/CONS h t))
% Assm: h4/string/SUB__def: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% Assm: h4/string/SUBSTRING__def: !s n i. h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i n)) = h4/rich__list/SEG n i s
% Assm: h4/string/TOCHAR__ind: !P. (!c. P (h4/list/CONS c h4/list/NIL)) /\ P h4/list/NIL /\ (!v6 v4 v5. P (h4/list/CONS v6 (h4/list/CONS v4 v5))) ==> (!v. P v)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% 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/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/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/rich__list/SPLITP0_c1: !x l P. h4/rich__list/SPLITP P (h4/list/CONS x l) = h4/bool/COND (P x) (h4/pair/_2C h4/list/NIL (h4/list/CONS x l)) (h4/pair/_2C (h4/list/CONS x (h4/pair/FST (h4/rich__list/SPLITP P l))) (h4/pair/SND (h4/rich__list/SPLITP P l)))
% Assm: h4/rich__list/SPLITP0_c0: !P. h4/rich__list/SPLITP P h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/list/NOT__NIL__CONS: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/LESS__EQ__MONO: !n m. h4/arithmetic/_3C_3D (h4/num/SUC n) (h4/num/SUC m) <=> h4/arithmetic/_3C_3D n m
% Assm: h4/list/TL0: !t h. h4/list/TL (h4/list/CONS h t) = t
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/bool/LET__CONG: !g f N M. M = N /\ (!x. x = N ==> f x = g x) ==> h4/bool/LET f M = h4/bool/LET g N
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D 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/list/NULL__EQ: !l. h4/list/NULL l <=> l = h4/list/NIL
% 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/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/prim__rec/WF__measure: !m. h4/relation/WF (h4/prim__rec/measure m)
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/prim__rec/measure__def: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% 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/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/string/STR__def: !c. h4/string/STR c = h4/list/CONS c h4/list/NIL
% Assm: h4/string/FIELDS__def_c0: !P. h4/string/FIELDS P h4/list/NIL = h4/list/CONS h4/list/NIL h4/list/NIL
% Assm: h4/string/TOCHAR__def: !c. h4/string/TOCHAR (h4/list/CONS c h4/list/NIL) = c
% Assm: h4/string/TOKENS__def_c0: !P. h4/string/TOKENS P h4/list/NIL = h4/list/NIL
% Assm: h4/string/char__nchotomy: !c. ?n. c = h4/string/CHR n
% Assm: h4/string/CHR__ORD: !a. h4/string/CHR (h4/string/ORD a) = a
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/arithmetic/LESS__TRANS: !p n m. h4/prim__rec/_3C m n /\ h4/prim__rec/_3C n p ==> h4/prim__rec/_3C m p
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> 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/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/arithmetic/LESS__MONO__EQ: !n m. h4/prim__rec/_3C (h4/num/SUC m) (h4/num/SUC n) <=> h4/prim__rec/_3C m n
% Assm: h4/prim__rec/LESS__REFL: !n. ~h4/prim__rec/_3C n n
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Goal: !cs. ?s. cs = h4/string/EXPLODE s
%   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_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (h4/list/CONS a0 a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_strings_EXPLODEu_u_defu_c1]: !s c. h4/string/EXPLODE (h4/list/CONS c s) = h4/list/CONS c (h4/string/EXPLODE s)
% Assm [h4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c0]: !s. h4/string/EXPLODE s = s
% Assm [h4s_strings_IMPLODEu_u_EXPLODE]: !s. h4/string/IMPLODE (h4/string/EXPLODE s) = s
% Assm [h4s_strings_EXPLODEu_u_defu_c0]: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_strings_IMPLODEu_u_defu_c1]: !cs c. h4/string/IMPLODE (h4/list/CONS c cs) = h4/list/CONS c (h4/string/IMPLODE cs)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_strings_IMPLODEu_u_defu_c0]: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% 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_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_strings_EXPLODEu_u_IMPLODE]: !cs. h4/string/EXPLODE (h4/string/IMPLODE cs) = cs
% Assm [h4s_strings_FIELDSu_u_curriedu_u_def]: !x1 x. h4/string/FIELDS x x1 = happ h4/string/FIELDS__tupled (h4/pair/_2C x x1)
% Assm [h4s_strings_FIELDSu_u_tupledu_u_primitiveu_u_def]: !_8. (!l FIELDS__tupled P r. happ (happ (happ (happ _8 l) FIELDS__tupled) P) r = h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (happ FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (happ FIELDS__tupled (h4/pair/_2C P (h4/list/TL r)))))) ==> (!_7. (!FIELDS__tupled P l. happ (happ (happ _7 FIELDS__tupled) P) l = happ (happ (happ _8 l) FIELDS__tupled) P) ==> (!_6. (!FIELDS__tupled P h t. happ (happ (happ (happ _6 FIELDS__tupled) P) h) t = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ _7 FIELDS__tupled) P)) (h4/rich__list/SPLITP P (h4/list/CONS h t)))) ==> (!_5. (!FIELDS__tupled P h. happ (happ (happ _5 FIELDS__tupled) P) h = happ (happ (happ _6 FIELDS__tupled) P) h) ==> (!_4. (!FIELDS__tupled P v1. happ (happ (happ _4 FIELDS__tupled) P) v1 = h4/list/list__CASE v1 (h4/combin/I (h4/list/CONS h4/list/NIL h4/list/NIL)) (happ (happ _5 FIELDS__tupled) P)) ==> (!_3. (!FIELDS__tupled P. happ (happ _3 FIELDS__tupled) P = happ (happ _4 FIELDS__tupled) P) ==> (!_2. (!FIELDS__tupled a. happ (happ _2 FIELDS__tupled) a = h4/pair/pair__CASE a (happ _3 FIELDS__tupled)) ==> (!_1. (!FIELDS__tupled. happ _1 FIELDS__tupled = happ _2 FIELDS__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t)))) ==> h4/string/FIELDS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_strings_TOKENSu_u_tupledu_u_primitiveu_u_def]: !_8. (!l TOKENS__tupled P r. happ (happ (happ (happ _8 l) TOKENS__tupled) P) r = h4/bool/COND (h4/list/NULL l) (happ TOKENS__tupled (h4/pair/_2C P (h4/list/TL r))) (h4/list/CONS l (happ TOKENS__tupled (h4/pair/_2C P r)))) ==> (!_7. (!TOKENS__tupled P l. happ (happ (happ _7 TOKENS__tupled) P) l = happ (happ (happ _8 l) TOKENS__tupled) P) ==> (!_6. (!TOKENS__tupled P h t. happ (happ (happ (happ _6 TOKENS__tupled) P) h) t = h4/combin/I (h4/bool/LET (h4/pair/UNCURRY (happ (happ _7 TOKENS__tupled) P)) (h4/rich__list/SPLITP P (h4/list/CONS h t)))) ==> (!_5. (!TOKENS__tupled P h. happ (happ (happ _5 TOKENS__tupled) P) h = happ (happ (happ _6 TOKENS__tupled) P) h) ==> (!_4. (!TOKENS__tupled P v1. happ (happ (happ _4 TOKENS__tupled) P) v1 = h4/list/list__CASE v1 (h4/combin/I h4/list/NIL) (happ (happ _5 TOKENS__tupled) P)) ==> (!_3. (!TOKENS__tupled P. happ (happ _3 TOKENS__tupled) P = happ (happ _4 TOKENS__tupled) P) ==> (!_2. (!TOKENS__tupled a. happ (happ _2 TOKENS__tupled) a = h4/pair/pair__CASE a (happ _3 TOKENS__tupled)) ==> (!_1. (!TOKENS__tupled. happ _1 TOKENS__tupled = happ _2 TOKENS__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (h4/list/CONS h t))) /\ (!t h P l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> happ (happ R (h4/pair/_2C P r)) (h4/pair/_2C P (h4/list/CONS h t)))) ==> h4/string/TOKENS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% Assm [h4s_strings_TOKENSu_u_curriedu_u_def]: !x1 x. h4/string/TOKENS x x1 = happ h4/string/TOKENS__tupled (h4/pair/_2C x x1)
% Assm [h4s_strings_TOCHARu_u_primitiveu_u_def]: !_6. (!v3. happ _6 v3 = h4/bool/ARB) ==> (!_5. (!v2. happ _5 v2 = _6) ==> (!_4. (!c v1. happ (happ _4 c) v1 = h4/list/list__CASE v1 (h4/combin/I c) _5) ==> (!_3. (!c. happ _3 c = happ _4 c) ==> (!_2. (!a. happ _2 a = h4/list/list__CASE a h4/bool/ARB _3) ==> (!_1. (!TOCHAR. happ _1 TOCHAR = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/string/TOCHAR = h4/relation/WFREC (h4/min/_40 _0) _1))))))
% Assm [h4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c1]: !s. h4/string/IMPLODE s = s
% Assm [h4s_strings_FIELDSu_u_defu_c1]: !_1. (!l P r. happ (happ (happ _1 l) P) r = h4/bool/COND (h4/list/NULL l) (h4/list/CONS h4/list/NIL (h4/string/FIELDS P (h4/list/TL r))) (h4/bool/COND (h4/list/NULL r) (h4/list/CONS l h4/list/NIL) (h4/list/CONS l (h4/string/FIELDS P (h4/list/TL r))))) ==> (!_0. (!P l. happ (happ _0 P) l = happ (happ _1 l) P) ==> (!t h P. h4/string/FIELDS P (h4/list/CONS h t) = h4/bool/LET (h4/pair/UNCURRY (happ _0 P)) (h4/rich__list/SPLITP P (h4/list/CONS h t))))
% Assm [h4s_strings_FIELDSu_u_ind]: !P_27. (!P. happ (happ P_27 P) h4/list/NIL) /\ (!P h t. (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ P_27 P) (h4/list/TL r)) /\ (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l /\ ~h4/list/NULL r ==> happ (happ P_27 P) (h4/list/TL r)) ==> happ (happ P_27 P) (h4/list/CONS h t)) ==> (!v v1. happ (happ P_27 v) v1)
% Assm [h4s_strings_TRANSLATEu_u_def]: !s f. h4/string/TRANSLATE f s = h4/list/FLAT (h4/list/MAP f s)
% Assm [h4s_strings_TOKENSu_u_ind]: !P_27. (!P. happ (happ P_27 P) h4/list/NIL) /\ (!P h t. (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ h4/list/NULL l ==> happ (happ P_27 P) (h4/list/TL r)) /\ (!l r. h4/pair/_2C l r = h4/rich__list/SPLITP P (h4/list/CONS h t) /\ ~h4/list/NULL l ==> happ (happ P_27 P) r) ==> happ (happ P_27 P) (h4/list/CONS h t)) ==> (!v v1. happ (happ P_27 v) v1)
% Assm [h4s_strings_TOKENSu_u_defu_c1]: !_1. (!l P r. happ (happ (happ _1 l) P) r = h4/bool/COND (h4/list/NULL l) (h4/string/TOKENS P (h4/list/TL r)) (h4/list/CONS l (h4/string/TOKENS P r))) ==> (!_0. (!P l. happ (happ _0 P) l = happ (happ _1 l) P) ==> (!t h P. h4/string/TOKENS P (h4/list/CONS h t) = h4/bool/LET (h4/pair/UNCURRY (happ _0 P)) (h4/rich__list/SPLITP P (h4/list/CONS h t))))
% Assm [h4s_strings_SUBu_u_def]: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% Assm [h4s_strings_SUBSTRINGu_u_def]: !s n i. h4/string/SUBSTRING (h4/pair/_2C s (h4/pair/_2C i n)) = h4/rich__list/SEG n i s
% Assm [h4s_strings_TOCHARu_u_ind]: !P. (!c. happ P (h4/list/CONS c h4/list/NIL)) /\ happ P h4/list/NIL /\ (!v6 v4 v5. happ P (h4/list/CONS v6 (h4/list/CONS v4 v5))) ==> (!v. happ P v)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% 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_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_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_richu_u_lists_SPLITP0u_c1]: !x l P. h4/rich__list/SPLITP P (h4/list/CONS x l) = h4/bool/COND (happ P x) (h4/pair/_2C h4/list/NIL (h4/list/CONS x l)) (h4/pair/_2C (h4/list/CONS x (h4/pair/FST (h4/rich__list/SPLITP P l))) (h4/pair/SND (h4/rich__list/SPLITP P l)))
% Assm [h4s_richu_u_lists_SPLITP0u_c0]: !P. h4/rich__list/SPLITP P h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_lists_NOTu_u_NILu_u_CONS]: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_MONO]: !n m. h4/arithmetic/_3C_3D (h4/num/SUC n) (h4/num/SUC m) <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_lists_TL0]: !t h. h4/list/TL (h4/list/CONS h t) = t
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_bools_LETu_u_CONG]: !g f N M. M = N /\ (!x. x = N ==> happ f x = happ g x) ==> h4/bool/LET f M = h4/bool/LET g N
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_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_lists_NULLu_u_EQ]: !l. h4/list/NULL l <=> l = h4/list/NIL
% 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_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_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_primu_u_recs_WFu_u_measure]: !m. h4/relation/WF (happ h4/prim__rec/measure m)
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_primu_u_recs_measureu_u_def]: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% 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_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (happ (h4/relation/inv__image R) f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% 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_combins_ou_u_DEF]: !g f x. h4/combin/o f g x = happ f (happ g x)
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_strings_STRu_u_def]: !c. h4/string/STR c = h4/list/CONS c h4/list/NIL
% Assm [h4s_strings_FIELDSu_u_defu_c0]: !P. h4/string/FIELDS P h4/list/NIL = h4/list/CONS h4/list/NIL h4/list/NIL
% Assm [h4s_strings_TOCHARu_u_def]: !c. happ h4/string/TOCHAR (h4/list/CONS c h4/list/NIL) = c
% Assm [h4s_strings_TOKENSu_u_defu_c0]: !P. h4/string/TOKENS P h4/list/NIL = h4/list/NIL
% Assm [h4s_strings_charu_u_nchotomy]: !c. ?n. c = h4/string/CHR n
% Assm [h4s_strings_CHRu_u_ORD]: !a. h4/string/CHR (h4/string/ORD a) = a
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_arithmetics_LESSu_u_TRANS]: !p n m. happ (happ h4/prim__rec/_3C m) n /\ happ (happ h4/prim__rec/_3C n) p ==> happ (happ h4/prim__rec/_3C m) p
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> 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_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% 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_EQu_u_REFL]: !x. x = x
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C (h4/num/SUC m)) (h4/num/SUC n) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_primu_u_recs_LESSu_u_REFL]: !n. ~happ (happ h4/prim__rec/_3C n) n
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Goal: !cs. ?s. cs = h4/string/EXPLODE s
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_Q1303025,TV_Q1303021]: ![V_f, V_g]: (![V_x]: s(TV_Q1303021,happ(s(t_fun(TV_Q1303025,TV_Q1303021),V_f),s(TV_Q1303025,V_x))) = s(TV_Q1303021,happ(s(t_fun(TV_Q1303025,TV_Q1303021),V_g),s(TV_Q1303025,V_x))) => s(t_fun(TV_Q1303025,TV_Q1303021),V_f) = s(t_fun(TV_Q1303025,TV_Q1303021),V_g))).
fof(ah4s_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_strings_EXPLODEu_u_defu_c1, axiom, ![V_s, V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),V_s))))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c0, axiom, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),V_s)).
fof(ah4s_strings_IMPLODEu_u_EXPLODE, axiom, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))))) = s(t_h4s_lists_list(t_h4s_strings_char),V_s)).
fof(ah4s_strings_EXPLODEu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_strings_IMPLODEu_u_defu_c1, axiom, ![V_cs, V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),V_cs))))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_cs)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_strings_IMPLODEu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_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_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (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_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
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,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),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_strings_EXPLODEu_u_IMPLODE, axiom, ![V_cs]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_cs))))) = s(t_h4s_lists_list(t_h4s_strings_char),V_cs)).
fof(ah4s_strings_FIELDSu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_fields(s(t_fun(t_h4s_strings_char,t_bool),V_x),s(t_h4s_lists_list(t_h4s_strings_char),V_x1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_fieldsu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_x),s(t_h4s_lists_list(t_h4s_strings_char),V_x1)))))).
fof(ah4s_strings_FIELDSu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_l, V_FIELDSu_u_tupled, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))))))) => ![V_uu_7]: (![V_FIELDSu_u_tupled, V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_6]: (![V_FIELDSu_u_tupled, V_P, V_h, V_t]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))),s(t_h4s_lists_list(t_h4s_strings_char),V_t))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) => ![V_uu_5]: (![V_FIELDSu_u_tupled, V_P, V_h]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) => ![V_uu_4]: (![V_FIELDSu_u_tupled, V_P, V_v1]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_v1),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))))),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))) => ![V_uu_3]: (![V_FIELDSu_u_tupled, V_P]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_2]: (![V_FIELDSu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a),s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))))) => ![V_uu_1]: (![V_FIELDSu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_FIELDSu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) & (![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) & ![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & (~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_fieldsu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1))))))))))))).
fof(ah4s_strings_TOKENSu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_8]: (![V_l, V_TOKENSu_u_tupled, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))) => ![V_uu_7]: (![V_TOKENSu_u_tupled, V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_8),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_6]: (![V_TOKENSu_u_tupled, V_P, V_h, V_t]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))),s(t_h4s_lists_list(t_h4s_strings_char),V_t))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) => ![V_uu_5]: (![V_TOKENSu_u_tupled, V_P, V_h]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_strings_char,V_h))) => ![V_uu_4]: (![V_TOKENSu_u_tupled, V_P, V_v1]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_v1),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_combins_i(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))))) => ![V_uu_3]: (![V_TOKENSu_u_tupled, V_P]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_uu_2]: (![V_TOKENSu_u_tupled, V_a]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),V_a),s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))))) => ![V_uu_1]: (![V_TOKENSu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),V_TOKENSu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R)))) & (![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))))) & ![V_t, V_h, V_P, V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_r))))),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_tokensu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),V_uu_1))))))))))))).
fof(ah4s_strings_TOKENSu_u_curriedu_u_def, axiom, ![V_x1, V_x]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_tokens(s(t_fun(t_h4s_strings_char,t_bool),V_x),s(t_h4s_lists_list(t_h4s_strings_char),V_x1))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_tokensu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_strings_char,t_bool),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_fun(t_h4s_strings_char,t_bool),V_x),s(t_h4s_lists_list(t_h4s_strings_char),V_x1)))))).
fof(ah4s_strings_TOCHARu_u_primitiveu_u_def, axiom, ![V_uu_6]: (![V_v3]: s(t_h4s_strings_char,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),V_uu_6),s(t_h4s_lists_list(t_h4s_strings_char),V_v3))) = s(t_h4s_strings_char,h4s_bools_arb) => ![V_uu_5]: (![V_v2]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_5),s(t_h4s_strings_char,V_v2))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),V_uu_6) => ![V_uu_4]: (![V_c, V_v1]: s(t_h4s_strings_char,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_4),s(t_h4s_strings_char,V_c))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1))) = s(t_h4s_strings_char,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_v1),s(t_h4s_strings_char,h4s_combins_i(s(t_h4s_strings_char,V_c))),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_5))) => ![V_uu_3]: (![V_c]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_3),s(t_h4s_strings_char,V_c))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_4),s(t_h4s_strings_char,V_c))) => ![V_uu_2]: (![V_a]: s(t_h4s_strings_char,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),V_uu_2),s(t_h4s_lists_list(t_h4s_strings_char),V_a))) = s(t_h4s_strings_char,h4s_lists_listu_u_case(s(t_h4s_lists_list(t_h4s_strings_char),V_a),s(t_h4s_strings_char,h4s_bools_arb),s(t_fun(t_h4s_strings_char,t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_3))) => ![V_uu_1]: (![V_TOCHAR]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_1),s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),V_TOCHAR))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_R))) => s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),h4s_strings_tochar) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),h4s_relations_wfrec(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char)),V_uu_1))))))))))).
fof(ah4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c1, axiom, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),V_s)).
fof(ah4s_strings_FIELDSu_u_defu_c1, axiom, ![V_uu_1]: (![V_l, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_1),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_fields(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_fields(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))))))) => ![V_uu_0]: (![V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_0),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_1),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_t, V_h, V_P]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_fields(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_0),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))).
fof(ah4s_strings_FIELDSu_u_ind, axiom, ![V_Pu_27]: ((![V_P]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)))) & ![V_P, V_h, V_t]: ((![V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) & ![V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & (~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_v))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1)))))).
fof(ah4s_strings_TRANSLATEu_u_def, axiom, ![V_s, V_f]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_translate(s(t_fun(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),V_f),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_map(s(t_fun(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),V_f),s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_strings_TOKENSu_u_ind, axiom, ![V_Pu_27]: ((![V_P]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)))) & ![V_P, V_h, V_t]: ((![V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) & ![V_l, V_r]: ((s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) & ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool)),V_Pu_27),s(t_fun(t_h4s_strings_char,t_bool),V_v))),s(t_h4s_lists_list(t_h4s_strings_char),V_v1)))))).
fof(ah4s_strings_TOKENSu_u_defu_c1, axiom, ![V_uu_1]: (![V_l, V_P, V_r]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_1),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_r))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_tokens(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_tl(s(t_h4s_lists_list(t_h4s_strings_char),V_r))))),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),V_l),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_tokens(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_r))))))) => ![V_uu_0]: (![V_P, V_l]: s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_0),s(t_fun(t_h4s_strings_char,t_bool),V_P))),s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_1),s(t_h4s_lists_list(t_h4s_strings_char),V_l))),s(t_fun(t_h4s_strings_char,t_bool),V_P))) => ![V_t, V_h, V_P]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_tokens(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)))),happ(s(t_fun(t_fun(t_h4s_strings_char,t_bool),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char))))),V_uu_0),s(t_fun(t_h4s_strings_char,t_bool),V_P))))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_lists_list(t_h4s_strings_char)),h4s_richu_u_lists_splitp(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_h),s(t_h4s_lists_list(t_h4s_strings_char),V_t)))))))))).
fof(ah4s_strings_SUBu_u_def, axiom, ![V_s, V_n]: s(t_h4s_strings_char,h4s_strings_sub(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_nums_num,V_n))))) = s(t_h4s_strings_char,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_h4s_strings_char),V_s)))).
fof(ah4s_strings_SUBSTRINGu_u_def, axiom, ![V_s, V_n, V_i]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_substring(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_strings_char),V_s),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_richu_u_lists_seg(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_i),s(t_h4s_lists_list(t_h4s_strings_char),V_s)))).
fof(ah4s_strings_TOCHARu_u_ind, axiom, ![V_P]: ((![V_c]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)))) & ![V_v6, V_v4, V_v5]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_v6),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_v4),s(t_h4s_lists_list(t_h4s_strings_char),V_v5)))))))))) => ![V_v]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),V_v)))))).
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_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_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (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_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => 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_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_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_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_lists_listu_u_nchotomy, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) | ?[V_h, V_t]: s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_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_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_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_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_bools_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_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_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_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_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_richu_u_lists_SPLITP0u_c1, axiom, ![TV_u_27a]: ![V_x, V_l, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))))))).
fof(ah4s_richu_u_lists_SPLITP0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_lists_NOTu_u_NILu_u_CONS, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = 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))))).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(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))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_MONO, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_lists_TL0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),V_t)).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_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_bools_LETu_u_CONG, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f, V_N, V_M]: ((s(TV_u_27a,V_M) = s(TV_u_27a,V_N) & ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_N) => 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_g),s(TV_u_27a,V_x))))) => s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_M))) = s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_N))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_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_lists_NULLu_u_EQ, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
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_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_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_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_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_primu_u_recs_WFu_u_measure, axiom, ![TV_u_27a]: ![V_m]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure),s(t_fun(TV_u_27a,t_h4s_nums_num),V_m))))))).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_primu_u_recs_measureu_u_def, axiom, ![TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure) = s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_invu_u_image(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c)))).
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_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_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)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),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_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_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_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_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_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_pairs_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_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_strings_STRu_u_def, axiom, ![V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_str(s(t_h4s_strings_char,V_c))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)))).
fof(ah4s_strings_FIELDSu_u_defu_c0, axiom, ![V_P]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_fields(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_cons(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil)))).
fof(ah4s_strings_TOCHARu_u_def, axiom, ![V_c]: s(t_h4s_strings_char,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_strings_char),h4s_strings_tochar),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))))) = s(t_h4s_strings_char,V_c)).
fof(ah4s_strings_TOKENSu_u_defu_c0, axiom, ![V_P]: s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_strings_tokens(s(t_fun(t_h4s_strings_char,t_bool),V_P),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_lists_list(t_h4s_strings_char)),h4s_lists_nil)).
fof(ah4s_strings_charu_u_nchotomy, axiom, ![V_c]: ?[V_n]: s(t_h4s_strings_char,V_c) = s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_n)))).
fof(ah4s_strings_CHRu_u_ORD, axiom, ![V_a]: s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_a))))) = s(t_h4s_strings_char,V_a)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_arithmetics_LESSu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_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_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_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_primu_u_recs_LESSu_u_REFL, axiom, ![V_n]: ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_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(ch4s_strings_EXPLODEu_u_ONTO, conjecture, ![V_cs]: ?[V_s]: s(t_h4s_lists_list(t_h4s_strings_char),V_cs) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))).
