%   ORIGINAL: h4/ASCIInumbers/s2n__compute
% 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/ASCIInumbers/s2n__def: !s f b. h4/ASCIInumbers/s2n b f s = h4/numposrep/l2n b (h4/list/MAP f (h4/list/REVERSE s))
% 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/bool/TRUTH: T
% Assm: h4/string/char__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))) rep
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/string/EXPLODE__def_c1: !s c. h4/string/EXPLODE (h4/list/CONS c s) = h4/list/CONS c (h4/string/EXPLODE s)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/string/EXPLODE__def_c0: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/string/IMPLODE__EXPLODE__I_c0: !s. h4/string/EXPLODE s = s
% Assm: h4/string/IMPLODE__EXPLODE: !s. h4/string/IMPLODE (h4/string/EXPLODE s) = s
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/ASCIInumbers/num__from__hex__string__def: h4/ASCIInumbers/num__from__hex__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/ASCIInumbers/UNHEX
% Assm: h4/ASCIInumbers/num__from__dec__string__def: h4/ASCIInumbers/num__from__dec__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/ASCIInumbers/UNHEX
% Assm: h4/ASCIInumbers/num__from__oct__string__def: h4/ASCIInumbers/num__from__oct__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/ASCIInumbers/UNHEX
% Assm: h4/ASCIInumbers/num__from__bin__string__def: h4/ASCIInumbers/num__from__bin__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/ASCIInumbers/UNHEX
% 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/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/string/EXPLODE__11: !s2 s1. h4/string/EXPLODE s1 = h4/string/EXPLODE s2 <=> s1 = s2
% Assm: h4/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/string/EXPLODE__IMPLODE: !cs. h4/string/EXPLODE (h4/string/IMPLODE cs) = cs
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/string/STRLEN__EXPLODE__THM: !s. h4/list/LENGTH s = h4/list/LENGTH (h4/string/EXPLODE s)
% Assm: h4/string/IMPLODE__EQ__THM_c1: !s l c. h4/string/IMPLODE l = h4/list/CONS c s <=> l = h4/list/CONS c (h4/string/EXPLODE s)
% Assm: h4/string/EXPLODE__EQ__THM_c1: !t s h. h4/string/EXPLODE s = h4/list/CONS h t <=> s = h4/list/CONS h (h4/string/IMPLODE t)
% Assm: h4/list/NOT__NIL__CONS: !a1 a0. ~(h4/list/NIL = h4/list/CONS a0 a1)
% Assm: h4/string/EXPLODE__EQNS_c1: !s c. h4/string/EXPLODE (h4/list/CONS c s) = h4/list/CONS c (h4/string/EXPLODE s)
% Assm: h4/string/IMPLODE__EQ__THM_c0: !s l c. h4/list/CONS c s = h4/string/IMPLODE l <=> l = h4/list/CONS c (h4/string/EXPLODE s)
% Assm: h4/string/EXPLODE__EQ__NIL_c0: !s. h4/string/EXPLODE s = h4/list/NIL <=> s = h4/list/NIL
% Assm: h4/string/EXPLODE__DEST__STRING: !s. h4/string/EXPLODE s = h4/option/option__CASE (h4/string/DEST__STRING s) h4/list/NIL (\v. h4/pair/pair__CASE v (\c t. h4/list/CONS c (h4/string/EXPLODE t)))
% Assm: h4/string/EXPLODE__EQ__NIL_c1: !s. h4/list/NIL = h4/string/EXPLODE s <=> s = h4/list/NIL
% Assm: h4/string/EXPLODE__ONTO: !cs. ?s. cs = h4/string/EXPLODE s
% Assm: h4/string/STRCAT__EXPLODE: !s2 s1. h4/list/APPEND s1 s2 = h4/list/FOLDR h4/list/CONS s2 (h4/string/EXPLODE s1)
% Assm: h4/string/EXPLODE__EQ__THM_c0: !t s h. h4/list/CONS h t = h4/string/EXPLODE s <=> s = h4/list/CONS h (h4/string/IMPLODE t)
% Assm: h4/string/IMPLODE__def_c1: !cs c. h4/string/IMPLODE (h4/list/CONS c cs) = h4/list/CONS c (h4/string/IMPLODE cs)
% Assm: h4/string/IMPLODE__def_c0: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/bool/AND__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_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/EQ__IMP__THM: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/string/EXPLODE__EQNS_c0: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/numposrep/l2n__dropWhile__0: !ls b. h4/prim__rec/_3C h4/num/0 b ==> h4/numposrep/l2n b (h4/list/REVERSE (h4/list/dropWhile ($equals h4/num/0) (h4/list/REVERSE ls))) = h4/numposrep/l2n b ls
% Assm: h4/numposrep/LOG__l2n__dropWhile: !l b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EXISTS (\y. ~(h4/num/0 = y)) l /\ h4/list/EVERY (h4/arithmetic/_3E b) l ==> h4/logroot/LOG b (h4/numposrep/l2n b l) = h4/prim__rec/PRE (h4/list/LENGTH (h4/list/dropWhile ($equals h4/num/0) (h4/list/REVERSE l)))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/string/DEST__STRING__def_c0: h4/string/DEST__STRING h4/list/NIL = h4/option/NONE
% Assm: h4/string/DEST__STRING__def_c1: !rst c. h4/string/DEST__STRING (h4/list/CONS c rst) = h4/option/SOME (h4/pair/_2C c rst)
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/option/option__case__def_c1: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/option/option__case__def_c0: !v f. h4/option/option__CASE h4/option/NONE v f = v
% 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/FOLDR0_c0: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/FOLDR0_c1: !x l f e. h4/list/FOLDR f e (h4/list/CONS x l) = f x (h4/list/FOLDR f e l)
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/numposrep/l2n__SNOC__0: !ls b. h4/prim__rec/_3C h4/num/0 b ==> h4/numposrep/l2n b (h4/list/SNOC h4/num/0 ls) = h4/numposrep/l2n b ls
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/list/dropWhile__DEF_c1: !t h P. h4/list/dropWhile P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/list/dropWhile P t) (h4/list/CONS h t)
% Assm: h4/list/dropWhile__DEF_c0: !P. h4/list/dropWhile P h4/list/NIL = h4/list/NIL
% Assm: h4/list/SNOC__APPEND: !x l. h4/list/SNOC x l = h4/list/APPEND l (h4/list/CONS x h4/list/NIL)
% Assm: h4/list/REVERSE__SNOC: !x l. h4/list/REVERSE (h4/list/SNOC x l) = h4/list/CONS x (h4/list/REVERSE l)
% Assm: h4/list/SNOC__INDUCT: !P. P h4/list/NIL /\ (!l. P l ==> (!x. P (h4/list/SNOC x l))) ==> (!l. P l)
% Assm: h4/list/REVERSE__REVERSE: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm: h4/list/REVERSE__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/REVERSE__DEF_c1: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/numposrep/LOG__l2n: !b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> (!l. ~(l = h4/list/NIL) /\ h4/prim__rec/_3C h4/num/0 (h4/list/LAST l) /\ h4/list/EVERY (h4/arithmetic/_3E b) l ==> h4/logroot/LOG b (h4/numposrep/l2n b l) = h4/prim__rec/PRE (h4/list/LENGTH l))
% Assm: h4/list/HD__dropWhile: !ls P. h4/list/EXISTS (h4/combin/o $not P) ls ==> ~P (h4/list/HD (h4/list/dropWhile P ls))
% Assm: h4/list/MEM__dropWhile__IMP: !x ls P. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/dropWhile P ls)) ==> h4/bool/IN x (h4/list/LIST__TO__SET ls)
% Assm: h4/rich__list/EVERY__REVERSE: !l P. h4/list/EVERY P (h4/list/REVERSE l) <=> h4/list/EVERY P l
% Assm: h4/list/dropWhile__eq__nil: !ls P. h4/list/dropWhile P ls = h4/list/NIL <=> h4/list/EVERY P ls
% Assm: h4/list/REVERSE__EQ__NIL: !l. h4/list/REVERSE l = h4/list/NIL <=> l = h4/list/NIL
% Assm: h4/list/LENGTH__REVERSE: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm: h4/list/MEM__REVERSE: !x l. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/REVERSE l)) <=> h4/bool/IN x (h4/list/LIST__TO__SET l)
% Assm: h4/list/LAST__REVERSE: !ls. ~(ls = h4/list/NIL) ==> h4/list/LAST (h4/list/REVERSE ls) = h4/list/HD ls
% Assm: h4/list/NOT__EVERY: !l P. ~h4/list/EVERY P l <=> h4/list/EXISTS (h4/combin/o $not P) l
% Assm: h4/list/EXISTS__MEM: !l P. h4/list/EXISTS P l <=> (?e. h4/bool/IN e (h4/list/LIST__TO__SET l) /\ P e)
% Assm: h4/list/EVERY__MEM: !l P. h4/list/EVERY P l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> P e)
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Goal: !s f b. h4/ASCIInumbers/s2n b f s = h4/numposrep/l2n b (h4/list/MAP f (h4/list/REVERSE (h4/string/EXPLODE s)))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_ASCIInumberss_s2nu_u_def]: !s f b. happ (h4/ASCIInumbers/s2n b f) s = h4/numposrep/l2n b (h4/list/MAP f (h4/list/REVERSE s))
% 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_bools_TRUTH]: T
% Assm [h4s_strings_charu_u_TYu_u_DEF]: !_0. (!n. happ _0 n <=> h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep)
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_strings_EXPLODEu_u_defu_c1]: !s c. h4/string/EXPLODE (happ (happ h4/list/CONS c) s) = happ (happ h4/list/CONS c) (h4/string/EXPLODE s)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_strings_EXPLODEu_u_defu_c0]: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c0]: !s. h4/string/EXPLODE s = s
% Assm [h4s_strings_IMPLODEu_u_EXPLODE]: !s. h4/string/IMPLODE (h4/string/EXPLODE s) = s
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_ASCIInumberss_numu_u_fromu_u_hexu_u_stringu_u_def]: h4/ASCIInumbers/num__from__hex__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) h4/ASCIInumbers/UNHEX
% Assm [h4s_ASCIInumberss_numu_u_fromu_u_decu_u_stringu_u_def]: h4/ASCIInumbers/num__from__dec__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/ASCIInumbers/UNHEX
% Assm [h4s_ASCIInumberss_numu_u_fromu_u_octu_u_stringu_u_def]: h4/ASCIInumbers/num__from__oct__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) h4/ASCIInumbers/UNHEX
% Assm [h4s_ASCIInumberss_numu_u_fromu_u_binu_u_stringu_u_def]: h4/ASCIInumbers/num__from__bin__string = h4/ASCIInumbers/s2n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/ASCIInumbers/UNHEX
% 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_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_strings_EXPLODEu_u_11]: !s2 s1. h4/string/EXPLODE s1 = h4/string/EXPLODE s2 <=> s1 = s2
% Assm [h4s_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = happ (happ h4/list/CONS h) t)
% Assm [h4s_strings_EXPLODEu_u_IMPLODE]: !cs. h4/string/EXPLODE (h4/string/IMPLODE cs) = cs
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_strings_STRLENu_u_EXPLODEu_u_THM]: !s. h4/list/LENGTH s = h4/list/LENGTH (h4/string/EXPLODE s)
% Assm [h4s_strings_IMPLODEu_u_EQu_u_THMu_c1]: !s l c. h4/string/IMPLODE l = happ (happ h4/list/CONS c) s <=> l = happ (happ h4/list/CONS c) (h4/string/EXPLODE s)
% Assm [h4s_strings_EXPLODEu_u_EQu_u_THMu_c1]: !t s h. h4/string/EXPLODE s = happ (happ h4/list/CONS h) t <=> s = happ (happ h4/list/CONS h) (h4/string/IMPLODE t)
% Assm [h4s_lists_NOTu_u_NILu_u_CONS]: !a1 a0. ~(h4/list/NIL = happ (happ h4/list/CONS a0) a1)
% Assm [h4s_strings_EXPLODEu_u_EQNSu_c1]: !s c. h4/string/EXPLODE (happ (happ h4/list/CONS c) s) = happ (happ h4/list/CONS c) (h4/string/EXPLODE s)
% Assm [h4s_strings_IMPLODEu_u_EQu_u_THMu_c0]: !s l c. happ (happ h4/list/CONS c) s = h4/string/IMPLODE l <=> l = happ (happ h4/list/CONS c) (h4/string/EXPLODE s)
% Assm [h4s_strings_EXPLODEu_u_EQu_u_NILu_c0]: !s. h4/string/EXPLODE s = h4/list/NIL <=> s = h4/list/NIL
% Assm [h4s_strings_EXPLODEu_u_DESTu_u_STRING]: !_2. (!c t. happ (happ _2 c) t = happ (happ h4/list/CONS c) (h4/string/EXPLODE t)) ==> (!_1. (!c. happ _1 c = happ _2 c) ==> (!_0. (!v. happ _0 v = h4/pair/pair__CASE v _1) ==> (!s. h4/string/EXPLODE s = h4/option/option__CASE (h4/string/DEST__STRING s) h4/list/NIL _0)))
% Assm [h4s_strings_EXPLODEu_u_EQu_u_NILu_c1]: !s. h4/list/NIL = h4/string/EXPLODE s <=> s = h4/list/NIL
% Assm [h4s_strings_EXPLODEu_u_ONTO]: !cs. ?s. cs = h4/string/EXPLODE s
% Assm [h4s_strings_STRCATu_u_EXPLODE]: !s2 s1. h4/list/APPEND s1 s2 = h4/list/FOLDR h4/list/CONS s2 (h4/string/EXPLODE s1)
% Assm [h4s_strings_EXPLODEu_u_EQu_u_THMu_c0]: !t s h. happ (happ h4/list/CONS h) t = h4/string/EXPLODE s <=> s = happ (happ h4/list/CONS h) (h4/string/IMPLODE t)
% Assm [h4s_strings_IMPLODEu_u_defu_c1]: !cs c. h4/string/IMPLODE (happ (happ h4/list/CONS c) cs) = happ (happ h4/list/CONS c) (h4/string/IMPLODE cs)
% Assm [h4s_strings_IMPLODEu_u_defu_c0]: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% 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_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_EQu_u_IMPu_u_THM]: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_strings_EXPLODEu_u_EQNSu_c0]: h4/string/EXPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_numposreps_l2nu_u_dropWhileu_u_0]: !ls b. h4/prim__rec/_3C h4/num/0 b ==> h4/numposrep/l2n b (h4/list/REVERSE (h4/list/dropWhile ($equals h4/num/0) (h4/list/REVERSE ls))) = h4/numposrep/l2n b ls
% Assm [h4s_numposreps_LOGu_u_l2nu_u_dropWhile]: !_0. (!y. happ _0 y <=> ~(h4/num/0 = y)) ==> (!l b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EXISTS _0 l /\ h4/list/EVERY (h4/arithmetic/_3E b) l ==> h4/logroot/LOG b (h4/numposrep/l2n b l) = h4/prim__rec/PRE (h4/list/LENGTH (h4/list/dropWhile ($equals h4/num/0) (h4/list/REVERSE l))))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_strings_DESTu_u_STRINGu_u_defu_c0]: h4/string/DEST__STRING h4/list/NIL = h4/option/NONE
% Assm [h4s_strings_DESTu_u_STRINGu_u_defu_c1]: !rst c. h4/string/DEST__STRING (happ (happ h4/list/CONS c) rst) = h4/option/SOME (h4/pair/_2C c rst)
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_options_optionu_u_caseu_u_defu_c1]: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = happ f x
% Assm [h4s_options_optionu_u_caseu_u_defu_c0]: !v f. h4/option/option__CASE h4/option/NONE v f = v
% 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_FOLDR0u_c0]: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_FOLDR0u_c1]: !x l f e. h4/list/FOLDR f e (happ (happ h4/list/CONS x) l) = happ (happ f x) (h4/list/FOLDR f e l)
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_numposreps_l2nu_u_SNOCu_u_0]: !ls b. h4/prim__rec/_3C h4/num/0 b ==> h4/numposrep/l2n b (h4/list/SNOC h4/num/0 ls) = h4/numposrep/l2n b ls
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_lists_dropWhileu_u_DEFu_c1]: !t h P. h4/list/dropWhile P (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (h4/list/dropWhile P t) (happ (happ h4/list/CONS h) t)
% Assm [h4s_lists_dropWhileu_u_DEFu_c0]: !P. h4/list/dropWhile P h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_SNOCu_u_APPEND]: !x l. h4/list/SNOC x l = h4/list/APPEND l (happ (happ h4/list/CONS x) h4/list/NIL)
% Assm [h4s_lists_REVERSEu_u_SNOC]: !x l. h4/list/REVERSE (h4/list/SNOC x l) = happ (happ h4/list/CONS x) (h4/list/REVERSE l)
% Assm [h4s_lists_SNOCu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!l. happ P l ==> (!x. happ P (h4/list/SNOC x l))) ==> (!l. happ P l)
% Assm [h4s_lists_REVERSEu_u_REVERSE]: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm [h4s_lists_REVERSEu_u_DEFu_c0]: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_REVERSEu_u_DEFu_c1]: !t h. h4/list/REVERSE (happ (happ h4/list/CONS h) t) = h4/list/APPEND (h4/list/REVERSE t) (happ (happ h4/list/CONS h) h4/list/NIL)
% 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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_numposreps_LOGu_u_l2n]: !b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b ==> (!l. ~(l = h4/list/NIL) /\ h4/prim__rec/_3C h4/num/0 (h4/list/LAST l) /\ h4/list/EVERY (h4/arithmetic/_3E b) l ==> h4/logroot/LOG b (h4/numposrep/l2n b l) = h4/prim__rec/PRE (h4/list/LENGTH l))
% Assm [h4s_lists_HDu_u_dropWhile]: !ls P. h4/list/EXISTS (h4/combin/o $not P) ls ==> ~happ P (h4/list/HD (h4/list/dropWhile P ls))
% Assm [h4s_lists_MEMu_u_dropWhileu_u_IMP]: !x ls P. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/dropWhile P ls)) ==> h4/bool/IN x (h4/list/LIST__TO__SET ls)
% Assm [h4s_richu_u_lists_EVERYu_u_REVERSE]: !l P. h4/list/EVERY P (h4/list/REVERSE l) <=> h4/list/EVERY P l
% Assm [h4s_lists_dropWhileu_u_equ_u_nil]: !ls P. h4/list/dropWhile P ls = h4/list/NIL <=> h4/list/EVERY P ls
% Assm [h4s_lists_REVERSEu_u_EQu_u_NIL]: !l. h4/list/REVERSE l = h4/list/NIL <=> l = h4/list/NIL
% Assm [h4s_lists_LENGTHu_u_REVERSE]: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm [h4s_lists_MEMu_u_REVERSE]: !x l. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/REVERSE l)) <=> h4/bool/IN x (h4/list/LIST__TO__SET l)
% Assm [h4s_lists_LASTu_u_REVERSE]: !ls. ~(ls = h4/list/NIL) ==> h4/list/LAST (h4/list/REVERSE ls) = h4/list/HD ls
% Assm [h4s_lists_NOTu_u_EVERY]: !l P. ~h4/list/EVERY P l <=> h4/list/EXISTS (h4/combin/o $not P) l
% Assm [h4s_lists_EXISTSu_u_MEM]: !l P. h4/list/EXISTS P l <=> (?e. h4/bool/IN e (h4/list/LIST__TO__SET l) /\ happ P e)
% Assm [h4s_lists_EVERYu_u_MEM]: !l P. h4/list/EVERY P l <=> (!e. h4/bool/IN e (h4/list/LIST__TO__SET l) ==> happ P e)
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Goal: !s f b. happ (h4/ASCIInumbers/s2n b f) s = h4/numposrep/l2n b (h4/list/MAP f (h4/list/REVERSE (h4/string/EXPLODE s)))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q1298217,TV_Q1298213]: ![V_f, V_g]: (![V_x]: s(TV_Q1298213,happ(s(t_fun(TV_Q1298217,TV_Q1298213),V_f),s(TV_Q1298217,V_x))) = s(TV_Q1298213,happ(s(t_fun(TV_Q1298217,TV_Q1298213),V_g),s(TV_Q1298217,V_x))) => s(t_fun(TV_Q1298217,TV_Q1298213),V_f) = s(t_fun(TV_Q1298217,TV_Q1298213),V_g))).
fof(ah4s_ASCIInumberss_s2nu_u_def, axiom, ![V_s, V_f, V_b]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f))),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))))).
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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_strings_charu_u_TYu_u_DEF, axiom, ![V_uu_0]: (![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_rep)))))).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_strings_EXPLODEu_u_defu_c1, axiom, ![V_s, V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),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),V_s))))) = 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_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_strings_EXPLODEu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_strings_IMPLODEu_u_EXPLODEu_u_Iu_c0, axiom, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),V_s)).
fof(ah4s_strings_IMPLODEu_u_EXPLODE, axiom, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))))) = s(t_h4s_lists_list(t_h4s_strings_char),V_s)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_ASCIInumberss_numu_u_fromu_u_hexu_u_stringu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_numu_u_fromu_u_hexu_u_string) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex)))).
fof(ah4s_ASCIInumberss_numu_u_fromu_u_decu_u_stringu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_numu_u_fromu_u_decu_u_string) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex)))).
fof(ah4s_ASCIInumberss_numu_u_fromu_u_octu_u_stringu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_numu_u_fromu_u_octu_u_string) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex)))).
fof(ah4s_ASCIInumberss_numu_u_fromu_u_binu_u_stringu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_numu_u_fromu_u_binu_u_string) = s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex)))).
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_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_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_strings_EXPLODEu_u_11, axiom, ![V_s2, V_s1]: (s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s1))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s2))) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_s1) = s(t_h4s_lists_list(t_h4s_strings_char),V_s2))).
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_strings_EXPLODEu_u_IMPLODE, axiom, ![V_cs]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_cs))))) = s(t_h4s_lists_list(t_h4s_strings_char),V_cs)).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
fof(ah4s_strings_STRLENu_u_EXPLODEu_u_THM, axiom, ![V_s]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_strings_IMPLODEu_u_EQu_u_THMu_c1, axiom, ![V_s, V_l, V_c]: (s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_l))) = 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),V_s))) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_l) = 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_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))))))).
fof(ah4s_strings_EXPLODEu_u_EQu_u_THMu_c1, axiom, ![V_t, V_s, V_h]: (s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),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_h4s_lists_list(t_h4s_strings_char),V_s) = 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),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))).
fof(ah4s_lists_NOTu_u_NILu_u_CONS, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),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))))).
fof(ah4s_strings_EXPLODEu_u_EQNSu_c1, axiom, ![V_s, V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),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),V_s))))) = 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_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_strings_IMPLODEu_u_EQu_u_THMu_c0, axiom, ![V_s, V_l, V_c]: (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),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_l))) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_l) = 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_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))))))).
fof(ah4s_strings_EXPLODEu_u_EQu_u_NILu_c0, axiom, ![V_s]: (s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_s) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))).
fof(ah4s_strings_EXPLODEu_u_DESTu_u_STRING, axiom, ![V_uu_2]: (![V_c, V_t]: 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))),V_uu_2),s(t_h4s_strings_char,V_c))),s(t_h4s_lists_list(t_h4s_strings_char),V_t))) = 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_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_t))))) => ![V_uu_1]: (![V_c]: 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))),V_uu_1),s(t_h4s_strings_char,V_c))) = 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))),V_uu_2),s(t_h4s_strings_char,V_c))) => ![V_uu_0]: (![V_v]: s(t_h4s_lists_list(t_h4s_strings_char),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_strings_char)),V_uu_0),s(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),V_v))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),V_v),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))),V_uu_1))) => ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_options_optionu_u_case(s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil),s(t_fun(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),t_h4s_lists_list(t_h4s_strings_char)),V_uu_0))))))).
fof(ah4s_strings_EXPLODEu_u_EQu_u_NILu_c1, axiom, ![V_s]: (s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_s) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))).
fof(ah4s_strings_EXPLODEu_u_ONTO, axiom, ![V_cs]: ?[V_s]: s(t_h4s_lists_list(t_h4s_strings_char),V_cs) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))).
fof(ah4s_strings_STRCATu_u_EXPLODE, axiom, ![V_s2, V_s1]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_append(s(t_h4s_lists_list(t_h4s_strings_char),V_s1),s(t_h4s_lists_list(t_h4s_strings_char),V_s2))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_foldr(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_lists_list(t_h4s_strings_char),V_s2),s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s1)))))).
fof(ah4s_strings_EXPLODEu_u_EQu_u_THMu_c0, axiom, ![V_t, V_s, V_h]: (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_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) <=> s(t_h4s_lists_list(t_h4s_strings_char),V_s) = 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),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_t))))))).
fof(ah4s_strings_IMPLODEu_u_defu_c1, axiom, ![V_cs, V_c]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),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),V_cs))))) = 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_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),V_cs)))))).
fof(ah4s_strings_IMPLODEu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_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_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_IMPu_u_THM, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) & (p(s(t_bool,V_t2)) => p(s(t_bool,V_t1)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f0) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_strings_EXPLODEu_u_EQNSu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_numposreps_l2nu_u_dropWhileu_u_0, axiom, ![V_ls, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_b)))) => s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_dropwhile(s(t_fun(t_h4s_nums_num,t_bool),d_equals(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_nums_num),V_ls))))))))) = s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_ls))))).
fof(ah4s_numposreps_LOGu_u_l2nu_u_dropWhile, axiom, ![V_uu_0]: (![V_y]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_y)))) <=> ~ (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,V_y))) => ![V_l, V_b]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) & (p(s(t_bool,h4s_lists_exists(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_lists_list(t_h4s_nums_num),V_l)))) & p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(s(t_h4s_nums_num,V_b))),s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))) => s(t_h4s_nums_num,h4s_logroots_log(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))) = s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_dropwhile(s(t_fun(t_h4s_nums_num,t_bool),d_equals(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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,f0))))).
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_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> 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,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
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,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_strings_DESTu_u_STRINGu_u_defu_c0, axiom, s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_options_none)).
fof(ah4s_strings_DESTu_u_STRINGu_u_defu_c1, axiom, ![V_rst, V_c]: s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_strings_destu_u_string(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),V_rst))))) = s(t_h4s_options_option(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char))),h4s_options_some(s(t_h4s_pairs_prod(t_h4s_strings_char,t_h4s_lists_list(t_h4s_strings_char)),h4s_pairs_u_2c(s(t_h4s_strings_char,V_c),s(t_h4s_lists_list(t_h4s_strings_char),V_rst)))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_options_optionu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_options_optionu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_none),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,V_v)).
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_FOLDR0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
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_lists_FOLDR0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),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(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_numposreps_l2nu_u_SNOCu_u_0, axiom, ![V_ls, V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_b)))) => s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_snoc(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(t_h4s_nums_num),V_ls))))) = s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_ls))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_lists_dropWhileu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_dropwhile(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_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_lists_list(TV_u_27a),h4s_lists_dropwhile(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))),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_dropWhileu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_dropwhile(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_SNOCu_u_APPEND, axiom, ![TV_u_27a]: ![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),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(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_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_lists_REVERSEu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(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),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_reverse(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_SNOCu_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_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)))) => ![V_x]: 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_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l)))))))) => ![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_REVERSEu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_REVERSEu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_REVERSEu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(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),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_t))),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)))))).
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_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_numposreps_LOGu_u_l2n, axiom, ![V_b]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_b)))) => ![V_l]: ((~ (s(t_h4s_lists_list(t_h4s_nums_num),V_l) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)) & (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_last(s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))) & p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(s(t_h4s_nums_num,V_b))),s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))) => s(t_h4s_nums_num,h4s_logroots_log(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))) = s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))))).
fof(ah4s_lists_HDu_u_dropWhile, axiom, ![TV_u_27a]: ![V_ls, V_P]: (p(s(t_bool,h4s_lists_exists(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_ls)))) => ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),h4s_lists_dropwhile(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_ls))))))))))).
fof(ah4s_lists_MEMu_u_dropWhileu_u_IMP, axiom, ![TV_u_27a]: ![V_x, V_ls, V_P]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_dropwhile(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_ls)))))))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_ls)))))))).
fof(ah4s_richu_u_lists_EVERYu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l, 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_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_dropWhileu_u_equ_u_nil, axiom, ![TV_u_27a]: ![V_ls, V_P]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_dropwhile(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_ls))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) <=> 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_ls)))))).
fof(ah4s_lists_REVERSEu_u_EQu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(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),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_lists_LENGTHu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(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),V_l)))).
fof(ah4s_lists_MEMu_u_REVERSE, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_LASTu_u_REVERSE, axiom, ![TV_u_27a]: ![V_ls]: (~ (s(t_h4s_lists_list(TV_u_27a),V_ls) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) => s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_ls))))) = s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_ls))))).
fof(ah4s_lists_NOTu_u_EVERY, axiom, ![TV_u_27a]: ![V_l, V_P]: (~ (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))) <=> p(s(t_bool,h4s_lists_exists(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_lists_EXISTSu_u_MEM, axiom, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> ?[V_e]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_e))))))).
fof(ah4s_lists_EVERYu_u_MEM, axiom, ![TV_u_27a]: ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> ![V_e]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_e))))))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f0)).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f0)).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_abbrev(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_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_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_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ch4s_ASCIInumberss_s2nu_u_compute, conjecture, ![V_s, V_f, V_b]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_asciinumberss_s2n(s(t_h4s_nums_num,V_b),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f))),s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),V_f),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_explode(s(t_h4s_lists_list(t_h4s_strings_char),V_s)))))))))).
