%   ORIGINAL: h4/ASCIInumbers/BIT__num__from__bin__string
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/list/LENGTH__MAP: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm: h4/list/EL__MAP: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> (!f. h4/list/EL n (h4/list/MAP f l) = f (h4/list/EL n l))
% Assm: h4/list/EVERY__MAP: !l f P. h4/list/EVERY P (h4/list/MAP f l) <=> h4/list/EVERY (\x. P (f x)) l
% Assm: h4/list/LENGTH__REVERSE: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm: h4/list/EL__REVERSE: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> h4/list/EL n (h4/list/REVERSE l) = h4/list/EL (h4/prim__rec/PRE (h4/arithmetic/_2D (h4/list/LENGTH l) n)) l
% Assm: h4/rich__list/EVERY__REVERSE: !l P. h4/list/EVERY P (h4/list/REVERSE l) <=> h4/list/EVERY P l
% Assm: h4/bit/BIT__def: !n b. h4/bit/BIT b n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bit/SUC__SUB: !a. h4/arithmetic/_2D (h4/num/SUC a) a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bit/BITS__THM: !n l h. h4/bit/BITS h l n = h4/arithmetic/MOD (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm: h4/numposrep/l2n__DIGIT: !x l b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EVERY (h4/arithmetic/_3E b) l /\ h4/prim__rec/_3C x (h4/list/LENGTH l) ==> h4/arithmetic/MOD (h4/arithmetic/DIV (h4/numposrep/l2n b l) (h4/arithmetic/EXP b x)) b = h4/list/EL x l
% Assm: h4/string/SUB__def: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% 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/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
% Goal: !x s. h4/list/EVERY (h4/combin/o (h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/ASCIInumbers/UNHEX) s /\ h4/prim__rec/_3C x (h4/list/LENGTH s) ==> (h4/bit/BIT x (h4/ASCIInumbers/num__from__bin__string s) <=> h4/ASCIInumbers/UNHEX (h4/string/SUB (h4/pair/_2C s (h4/prim__rec/PRE (h4/arithmetic/_2D (h4/list/LENGTH s) x)))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_arithmetics_EXPu_u_1u_c1]: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_lists_LENGTHu_u_MAP]: !l f. h4/list/LENGTH (h4/list/MAP f l) = h4/list/LENGTH l
% Assm [h4s_lists_ELu_u_MAP]: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> (!f. h4/list/EL n (h4/list/MAP f l) = happ f (h4/list/EL n l))
% Assm [h4s_lists_EVERYu_u_MAP]: !_0. (!P f x. happ (happ (happ _0 P) f) x <=> happ P (happ f x)) ==> (!l f P. h4/list/EVERY P (h4/list/MAP f l) <=> h4/list/EVERY (happ (happ _0 P) f) l)
% Assm [h4s_lists_LENGTHu_u_REVERSE]: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm [h4s_lists_ELu_u_REVERSE]: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> h4/list/EL n (h4/list/REVERSE l) = h4/list/EL (h4/prim__rec/PRE (h4/arithmetic/_2D (h4/list/LENGTH l) n)) l
% 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_bits_BITu_u_def]: !n b. h4/bit/BIT b n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bits_SUCu_u_SUB]: !a. h4/arithmetic/_2D (h4/num/SUC a) a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bits_BITSu_u_THM]: !n l h. h4/bit/BITS h l n = h4/arithmetic/MOD (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm [h4s_numposreps_l2nu_u_DIGIT]: !x l b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EVERY (h4/arithmetic/_3E b) l /\ h4/prim__rec/_3C x (h4/list/LENGTH l) ==> h4/arithmetic/MOD (h4/arithmetic/DIV (h4/numposrep/l2n b l) (h4/arithmetic/EXP b x)) b = h4/list/EL x l
% Assm [h4s_strings_SUBu_u_def]: !s n. h4/string/SUB (h4/pair/_2C s n) = h4/list/EL n s
% 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_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
% Goal: !x s. h4/list/EVERY (h4/combin/o (h4/arithmetic/_3E (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/ASCIInumbers/UNHEX) s /\ h4/prim__rec/_3C x (h4/list/LENGTH s) ==> (h4/bit/BIT x (happ h4/ASCIInumbers/num__from__bin__string s) <=> happ h4/ASCIInumbers/UNHEX (h4/string/SUB (h4/pair/_2C s (h4/prim__rec/PRE (h4/arithmetic/_2D (h4/list/LENGTH s) x)))) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q207742,TV_Q207738]: ![V_f, V_g]: (![V_x]: s(TV_Q207738,happ(s(t_fun(TV_Q207742,TV_Q207738),V_f),s(TV_Q207742,V_x))) = s(TV_Q207738,happ(s(t_fun(TV_Q207742,TV_Q207738),V_g),s(TV_Q207742,V_x))) => s(t_fun(TV_Q207742,TV_Q207738),V_f) = s(t_fun(TV_Q207742,TV_Q207738),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_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_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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_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_arithmetics_EXPu_u_1u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),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_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(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_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![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_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,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))))))).
fof(ah4s_lists_LENGTHu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_f]: s(t_h4s_nums_num,h4s_lists_length(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))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_ELu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => ![V_f]: s(TV_u_27b,h4s_lists_el(s(t_h4s_nums_num,V_n),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))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_lists_EVERYu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_P, V_f, V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))) => ![V_l, V_f, V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27b,t_bool),V_P),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))))) = s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
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_ELu_u_REVERSE, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(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_reverse(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_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,V_n))))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
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_bits_BITu_u_def, axiom, ![V_n, V_b]: (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n)))) <=> s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n))) = 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_bits_SUCu_u_SUB, axiom, ![V_a]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_a))) = 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_bits_BITSu_u_THM, axiom, ![V_n, V_l, V_h]: s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_exp(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_h4s_nums_num,V_l))))),s(t_h4s_nums_num,h4s_arithmetics_exp(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_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,V_l)))))))).
fof(ah4s_numposreps_l2nu_u_DIGIT, axiom, ![V_x, 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_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)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),V_l)))))))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_div(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_arithmetics_exp(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_x))))),s(t_h4s_nums_num,V_b))) = s(t_h4s_nums_num,h4s_lists_el(s(t_h4s_nums_num,V_x),s(t_h4s_lists_list(t_h4s_nums_num),V_l))))).
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_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_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(ch4s_ASCIInumberss_BITu_u_numu_u_fromu_u_binu_u_string, conjecture, ![V_x, V_s]: ((p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_strings_char,t_bool),h4s_combins_o(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_u_3e(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))),s(t_h4s_lists_list(t_h4s_strings_char),V_s)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),V_s))))))) => (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,happ(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_h4s_lists_list(t_h4s_strings_char),V_s)))))) <=> s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_asciinumberss_unhex),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,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_strings_char),V_s))),s(t_h4s_nums_num,V_x))))))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
