%   ORIGINAL: h4/string/TOKENS__ind
% 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/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/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% 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/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/TOKENS__curried__def: !x1 x. h4/string/TOKENS x x1 = h4/string/TOKENS__tupled (h4/pair/_2C x x1)
% Assm: h4/bool/TRUTH: T
% Assm: h4/rich__list/SPLITP__compute: h4/rich__list/SPLITP = h4/rich__list/SPLITP__AUX h4/list/NIL
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/list/TL0: !t h. h4/list/TL (h4/list/CONS h t) = t
% 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/SUB__def: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% Assm: h4/string/TRANSLATE__def: !s f. h4/string/TRANSLATE f s = h4/list/FLAT (h4/list/MAP f s)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/CONS1: !l. ~h4/list/NULL l ==> h4/list/CONS (h4/list/HD l) (h4/list/TL l) = l
% Assm: h4/rich__list/TL__SNOC: !x l. h4/list/TL (h4/list/SNOC x l) = h4/bool/COND (h4/list/NULL l) h4/list/NIL (h4/list/SNOC x (h4/list/TL l))
% Assm: h4/list/MAP__TL: !l f. ~h4/list/NULL l ==> h4/list/MAP f (h4/list/TL l) = h4/list/TL (h4/list/MAP f l)
% Assm: h4/list/list__case__compute: !l f b. h4/list/list__CASE l b f = h4/bool/COND (h4/list/NULL l) b (f (h4/list/HD l) (h4/list/TL l))
% Assm: h4/rich__list/SPLITP__EVERY: !l P. h4/list/EVERY (\x. ~P x) l ==> h4/rich__list/SPLITP P l = h4/pair/_2C l h4/list/NIL
% Assm: h4/rich__list/SPLITR__def: !l P. h4/rich__list/SPLITR P l = h4/bool/LET (h4/pair/UNCURRY (\a b. h4/pair/_2C (h4/list/REVERSE b) (h4/list/REVERSE a))) (h4/rich__list/SPLITP (h4/combin/o $not P) (h4/list/REVERSE l))
% Assm: h4/rich__list/SPLITL__def: !P. h4/rich__list/SPLITL P = h4/rich__list/SPLITP (h4/combin/o $not P)
% Assm: h4/rich__list/PREFIX__DEF: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (h4/rich__list/SPLITP (h4/combin/o $not P) l)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/list/LENGTH__TL: !l. h4/prim__rec/_3C h4/num/0 (h4/list/LENGTH l) ==> h4/list/LENGTH (h4/list/TL l) = h4/arithmetic/_2D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/list/EL__simp_c0: !n l. h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) l = h4/list/EL (h4/prim__rec/PRE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) (h4/list/TL l)
% Assm: h4/list/EL__simp_c1: !n l. h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) l = h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/list/TL l)
% Assm: h4/list/EL__compute: !n l. h4/list/EL n l = h4/bool/COND (n = h4/num/0) (h4/list/HD l) (h4/list/EL (h4/prim__rec/PRE n) (h4/list/TL l))
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% 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/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% 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/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/list/EL0_c1: !n l. h4/list/EL (h4/num/SUC n) l = h4/list/EL n (h4/list/TL l)
% Assm: h4/prim__rec/PRE0_c1: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/list/HD0: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/NULL0_c1: !t h. ~h4/list/NULL (h4/list/CONS h t)
% Assm: h4/list/NULL0_c0: h4/list/NULL h4/list/NIL
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/arithmetic/ADD__CLAUSES_c3: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/BIT20: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/arithmetic/BIT10: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm: h4/list/NULL__DEF_c1: !t h. h4/list/NULL (h4/list/CONS h t) <=> F
% Assm: h4/list/NULL__DEF_c0: h4/list/NULL h4/list/NIL <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% 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/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% 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__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/list/list__case__def_c1: !v f a1 a0. h4/list/list__CASE (h4/list/CONS a0 a1) v f = f a0 a1
% Assm: h4/list/list__case__def_c0: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm: h4/list/list__CASES: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/list/SNOC0_c1: !x_27 x l. h4/list/SNOC x (h4/list/CONS x_27 l) = h4/list/CONS x_27 (h4/list/SNOC x l)
% Assm: h4/list/SNOC0_c0: !x. h4/list/SNOC x h4/list/NIL = h4/list/CONS x h4/list/NIL
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/rich__list/SPLITP__AUX__def_c1: !t h acc P. h4/rich__list/SPLITP__AUX acc P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/pair/_2C acc (h4/list/CONS h t)) (h4/rich__list/SPLITP__AUX (h4/list/APPEND acc (h4/list/CONS h h4/list/NIL)) P t)
% Assm: h4/rich__list/SPLITP__AUX__def_c0: !acc P. h4/rich__list/SPLITP__AUX acc P h4/list/NIL = h4/pair/_2C acc h4/list/NIL
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/list/EL0_c0: !l. h4/list/EL h4/num/0 l = h4/list/HD l
% Assm: h4/prim__rec/PRE0_c0: h4/prim__rec/PRE h4/num/0 = h4/num/0
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/EVERY__DEF_c1: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> P h /\ h4/list/EVERY P t
% Assm: h4/list/EVERY__DEF_c0: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Goal: !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)
%   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_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))) (happ (happ 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)) (happ (happ h4/rich__list/SPLITP P) (happ (happ 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 = happ (happ h4/rich__list/SPLITP P) (happ (happ h4/list/CONS h) t) /\ h4/list/NULL l ==> happ (happ R (h4/pair/_2C P (h4/list/TL r))) (h4/pair/_2C P (happ (happ h4/list/CONS h) t))) /\ (!t h P l r. h4/pair/_2C l r = happ (happ h4/rich__list/SPLITP P) (happ (happ h4/list/CONS h) t) /\ ~h4/list/NULL l ==> happ (happ R (h4/pair/_2C P r)) (h4/pair/_2C P (happ (happ h4/list/CONS h) t)))) ==> h4/string/TOKENS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))
% 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_TOCHARu_u_ind]: !P. (!c. happ P (happ (happ h4/list/CONS c) h4/list/NIL)) /\ happ P h4/list/NIL /\ (!v6 v4 v5. happ P (happ (happ h4/list/CONS v6) (happ (happ h4/list/CONS v4) v5))) ==> (!v. happ P v)
% Assm [h4s_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (happ (happ h4/list/CONS a0) a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_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_bools_TRUTH]: T
% Assm [h4s_richu_u_lists_SPLITPu_u_compute]: h4/rich__list/SPLITP = h4/rich__list/SPLITP__AUX h4/list/NIL
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_lists_TL0]: !t h. h4/list/TL (happ (happ h4/list/CONS h) t) = t
% 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_SUBu_u_def]: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% Assm [h4s_strings_TRANSLATEu_u_def]: !s f. h4/string/TRANSLATE f s = h4/list/FLAT (h4/list/MAP f s)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_richu_u_lists_SPLITP0u_c1]: !x l P. happ (happ h4/rich__list/SPLITP P) (happ (happ h4/list/CONS x) l) = h4/bool/COND (happ P x) (h4/pair/_2C h4/list/NIL (happ (happ h4/list/CONS x) l)) (h4/pair/_2C (happ (happ h4/list/CONS x) (h4/pair/FST (happ (happ h4/rich__list/SPLITP P) l))) (h4/pair/SND (happ (happ h4/rich__list/SPLITP P) l)))
% Assm [h4s_richu_u_lists_SPLITP0u_c0]: !P. happ (happ h4/rich__list/SPLITP P) h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lists_CONS1]: !l. ~h4/list/NULL l ==> happ (happ h4/list/CONS (h4/list/HD l)) (h4/list/TL l) = l
% Assm [h4s_richu_u_lists_TLu_u_SNOC]: !x l. h4/list/TL (h4/list/SNOC x l) = h4/bool/COND (h4/list/NULL l) h4/list/NIL (h4/list/SNOC x (h4/list/TL l))
% Assm [h4s_lists_MAPu_u_TL]: !l f. ~h4/list/NULL l ==> h4/list/MAP f (h4/list/TL l) = h4/list/TL (h4/list/MAP f l)
% Assm [h4s_lists_listu_u_caseu_u_compute]: !l f b. h4/list/list__CASE l b f = h4/bool/COND (h4/list/NULL l) b (happ (happ f (h4/list/HD l)) (h4/list/TL l))
% Assm [h4s_richu_u_lists_SPLITPu_u_EVERY]: !_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!l P. h4/list/EVERY (happ _0 P) l ==> happ (happ h4/rich__list/SPLITP P) l = h4/pair/_2C l h4/list/NIL)
% Assm [h4s_richu_u_lists_SPLITRu_u_def]: !_1. (!a b. happ (happ _1 a) b = h4/pair/_2C (h4/list/REVERSE b) (h4/list/REVERSE a)) ==> (!_0. (!a. happ _0 a = happ _1 a) ==> (!l P. h4/rich__list/SPLITR P l = h4/bool/LET (h4/pair/UNCURRY _0) (happ (happ h4/rich__list/SPLITP (h4/combin/o $not P)) (h4/list/REVERSE l))))
% Assm [h4s_richu_u_lists_SPLITLu_u_def]: !P. h4/rich__list/SPLITL P = happ h4/rich__list/SPLITP (h4/combin/o $not P)
% Assm [h4s_richu_u_lists_PREFIXu_u_DEF]: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (happ (happ h4/rich__list/SPLITP (h4/combin/o $not P)) l)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_lists_LENGTHu_u_TL]: !l. h4/prim__rec/_3C h4/num/0 (h4/list/LENGTH l) ==> h4/list/LENGTH (h4/list/TL l) = h4/arithmetic/_2D (h4/list/LENGTH l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_lists_ELu_u_simpu_c0]: !n l. h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) l = h4/list/EL (h4/prim__rec/PRE (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) (h4/list/TL l)
% Assm [h4s_lists_ELu_u_simpu_c1]: !n l. h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) l = h4/list/EL (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) (h4/list/TL l)
% Assm [h4s_lists_ELu_u_compute]: !n l. ?v. (v <=> n = h4/num/0) /\ h4/list/EL n l = h4/bool/COND v (h4/list/HD l) (h4/list/EL (h4/prim__rec/PRE n) (h4/list/TL l))
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% 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_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = happ (happ h4/list/CONS h) t)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_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_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_lists_EL0u_c1]: !n l. h4/list/EL (h4/num/SUC n) l = h4/list/EL n (h4/list/TL l)
% Assm [h4s_primu_u_recs_PRE0u_c1]: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_lists_HD0]: !t h. h4/list/HD (happ (happ h4/list/CONS h) t) = h
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_lists_NULL0u_c1]: !t h. ~h4/list/NULL (happ (happ h4/list/CONS h) t)
% Assm [h4s_lists_NULL0u_c0]: h4/list/NULL h4/list/NIL
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c3]: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_BIT20]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_arithmetics_BIT10]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm [h4s_lists_NULLu_u_DEFu_c1]: !t h. h4/list/NULL (happ (happ h4/list/CONS h) t) <=> F
% Assm [h4s_lists_NULLu_u_DEFu_c0]: h4/list/NULL h4/list/NIL <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. happ (happ h4/list/CONS a0) a1 = happ (happ h4/list/CONS a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% 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_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_lists_listu_u_caseu_u_defu_c1]: !v f a1 a0. h4/list/list__CASE (happ (happ h4/list/CONS a0) a1) v f = happ (happ f a0) a1
% Assm [h4s_lists_listu_u_caseu_u_defu_c0]: !v f. h4/list/list__CASE h4/list/NIL v f = v
% Assm [h4s_lists_listu_u_CASES]: !l. l = h4/list/NIL \/ (?h t. l = happ (happ h4/list/CONS h) t)
% Assm [h4s_lists_SNOC0u_c1]: !x_27 x l. h4/list/SNOC x (happ (happ h4/list/CONS x_27) l) = happ (happ h4/list/CONS x_27) (h4/list/SNOC x l)
% Assm [h4s_lists_SNOC0u_c0]: !x. h4/list/SNOC x h4/list/NIL = happ (happ h4/list/CONS x) h4/list/NIL
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c1]: !t h acc P. happ (happ (h4/rich__list/SPLITP__AUX acc) P) (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (h4/pair/_2C acc (happ (happ h4/list/CONS h) t)) (happ (happ (h4/rich__list/SPLITP__AUX (h4/list/APPEND acc (happ (happ h4/list/CONS h) h4/list/NIL))) P) t)
% Assm [h4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c0]: !acc P. happ (happ (h4/rich__list/SPLITP__AUX acc) P) h4/list/NIL = h4/pair/_2C acc h4/list/NIL
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_lists_EL0u_c0]: !l. h4/list/EL h4/num/0 l = h4/list/HD l
% Assm [h4s_primu_u_recs_PRE0u_c0]: h4/prim__rec/PRE h4/num/0 = h4/num/0
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (happ f h)) (h4/list/MAP f t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_EVERYu_u_DEFu_c1]: !t h P. h4/list/EVERY P (happ (happ h4/list/CONS h) t) <=> happ P h /\ h4/list/EVERY P t
% Assm [h4s_lists_EVERYu_u_DEFu_c0]: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (happ (happ h4/list/CONS h) t) = h4/num/SUC (h4/list/LENGTH t)
% Goal: !P_27. (!P. happ (happ P_27 P) h4/list/NIL) /\ (!P h t. (!l r. h4/pair/_2C l r = happ (happ h4/rich__list/SPLITP P) (happ (happ 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 = happ (happ h4/rich__list/SPLITP P) (happ (happ h4/list/CONS h) t) /\ ~h4/list/NULL l ==> happ (happ P_27 P) r) ==> happ (happ P_27 P) (happ (happ h4/list/CONS h) t)) ==> (!v v1. happ (happ P_27 v) v1)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1302774,TV_Q1302770]: ![V_f, V_g]: (![V_x]: s(TV_Q1302770,happ(s(t_fun(TV_Q1302774,TV_Q1302770),V_f),s(TV_Q1302774,V_x))) = s(TV_Q1302770,happ(s(t_fun(TV_Q1302774,TV_Q1302770),V_g),s(TV_Q1302774,V_x))) => s(t_fun(TV_Q1302774,TV_Q1302770),V_f) = s(t_fun(TV_Q1302774,TV_Q1302770),V_g))).
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)),happ(s(t_fun(t_h4s_lists_list(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_lists_list(t_h4s_strings_char)),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)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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_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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_strings_char))),h4s_lists_cons),s(t_h4s_strings_char,V_v6))),s(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_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_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_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_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_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_richu_u_lists_SPLITPu_u_compute, axiom, ![TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
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_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_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,t0)))).
fof(ah4s_lists_TL0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),V_t)).
fof(ah4s_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_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_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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> 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)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_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)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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_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_CONS1, 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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l))).
fof(ah4s_richu_u_lists_TLu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l)))))))).
fof(ah4s_lists_MAPu_u_TL, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f]: (~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l))))) => s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_lists_listu_u_caseu_u_compute, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f, V_b]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),V_l),s(TV_u_27b,V_b),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l))),s(TV_u_27b,V_b),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,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l)))))))).
fof(ah4s_richu_u_lists_SPLITPu_u_EVERY, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),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,V_x)))))) => ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),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)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_richu_u_lists_SPLITRu_u_def, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_a, V_b]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_h4s_lists_list(TV_u_27a),V_a))),s(t_h4s_lists_list(TV_u_27a),V_b))) = 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_reverse(s(t_h4s_lists_list(TV_u_27a),V_b))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_a))))) => ![V_uu_0]: (![V_a]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_h4s_lists_list(TV_u_27a),V_a))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_h4s_lists_list(TV_u_27a),V_a))) => ![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_splitr(s(t_fun(TV_u_27a,t_bool),V_P),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_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l)))))))))).
fof(ah4s_richu_u_lists_SPLITLu_u_def, axiom, ![TV_u_27a]: ![V_P]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_splitl(s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_richu_u_lists_PREFIXu_u_DEF, axiom, ![TV_u_27a]: ![V_l, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_prefix(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_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),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),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P))))),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_LENGTHu_u_TL, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_lists_ELu_u_simpu_c0, axiom, ![TV_u_27a]: ![V_n, V_l]: s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_ELu_u_simpu_c1, axiom, ![TV_u_27a]: ![V_n, V_l]: s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_ELu_u_compute, axiom, ![TV_u_27a]: ![V_n, V_l]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_l))),s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
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,t0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
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_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))).
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_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_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_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_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_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_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_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_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_lists_EL0u_c1, axiom, ![TV_u_27a]: ![V_n, V_l]: s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),h4s_lists_tl(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_primu_u_recs_PRE0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t0)))).
fof(ah4s_lists_HD0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(TV_u_27a,V_h)).
fof(ah4s_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_NULL0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))).
fof(ah4s_lists_NULL0u_c0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))).
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,t0)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_BIT20, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_arithmetics_BIT10, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_lists_NULLu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_bool,f)).
fof(ah4s_lists_NULLu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t0)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t0))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_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_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_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_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_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_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_lists_listu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1)))).
fof(ah4s_lists_listu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_lists_listu_u_CASES, 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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))).
fof(ah4s_lists_SNOC0u_c1, axiom, ![TV_u_27a]: ![V_xu_27, V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_SNOC0u_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_acc, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),V_acc))),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = 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_h))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_acc),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_acc),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))))),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c0, axiom, ![TV_u_27a]: ![V_acc, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),V_acc))),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),V_acc),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_bools_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![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),V_g),s(TV_u_27a,V_x))))).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
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_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_EL0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_primu_u_recs_PRE0u_c0, axiom, s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_nums_NOTu_u_SUC, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_EVERYu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) & p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_EVERYu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t0)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_lists_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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ch4s_strings_TOKENSu_u_ind, conjecture, ![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)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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)),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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),happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_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)))))).
