%   ORIGINAL: h4/patricia__casts/string__to__num__11
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !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/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/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/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP__APPEND: !l2 l1 f. h4/list/MAP f (h4/list/APPEND l1 l2) = h4/list/APPEND (h4/list/MAP f l1) (h4/list/MAP f l2)
% 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/string/ORD__11: !a_27 a. h4/string/ORD a = h4/string/ORD a_27 <=> a = a_27
% Assm: h4/string/ORD__CHR__RWT: !r. h4/prim__rec/_3C r (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))))))))) ==> h4/string/ORD (h4/string/CHR r) = r
% 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/patricia__casts/string__to__num__def: !s. h4/patricia__casts/string__to__num s = h4/ASCIInumbers/s2n (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))))))))) h4/string/ORD (h4/list/CONS (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) s)
% Assm: h4/patricia__casts/l2n__11: !l2 l1 b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EVERY (h4/arithmetic/_3E b) l1 /\ h4/list/EVERY (h4/arithmetic/_3E b) l2 ==> (h4/numposrep/l2n b (h4/list/APPEND l1 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/list/NIL)) = h4/numposrep/l2n b (h4/list/APPEND l2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/list/NIL)) <=> l1 = l2)
% Assm: h4/patricia__casts/EVERY__MAP__ORD: !l. h4/list/EVERY (h4/arithmetic/_3E (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)))))))))) (h4/list/MAP h4/string/ORD l)
% Assm: h4/patricia__casts/MAP__11: !l2 l1 f. (!x y. f x = f y <=> x = y) ==> (h4/list/MAP f l1 = h4/list/MAP f l2 <=> l1 = l2)
% Assm: h4/patricia__casts/REVERSE__11: !l2 l1. h4/list/REVERSE l1 = h4/list/REVERSE l2 <=> l1 = l2
% Goal: !t s. h4/patricia__casts/string__to__num s = h4/patricia__casts/string__to__num t <=> s = t
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !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_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_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_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (happ f h) (h4/list/MAP f t)
% Assm [h4s_lists_MAPu_u_APPEND]: !l2 l1 f. h4/list/MAP f (h4/list/APPEND l1 l2) = h4/list/APPEND (h4/list/MAP f l1) (h4/list/MAP f l2)
% Assm [h4s_lists_REVERSEu_u_DEFu_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 [h4s_strings_ORDu_u_11]: !a_27 a. happ h4/string/ORD a = happ h4/string/ORD a_27 <=> a = a_27
% Assm [h4s_strings_ORDu_u_CHRu_u_RWT]: !r. h4/prim__rec/_3C r (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))))))))) ==> happ h4/string/ORD (h4/string/CHR r) = r
% Assm [h4s_ASCIInumberss_s2nu_u_def]: !s f b. h4/ASCIInumbers/s2n b f s = h4/numposrep/l2n b (h4/list/MAP f (h4/list/REVERSE s))
% Assm [h4s_patriciau_u_castss_stringu_u_tou_u_numu_u_def]: !s. h4/patricia__casts/string__to__num s = h4/ASCIInumbers/s2n (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))))))))) h4/string/ORD (h4/list/CONS (h4/string/CHR (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) s)
% Assm [h4s_patriciau_u_castss_l2nu_u_11]: !l2 l1 b. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) b /\ h4/list/EVERY (h4/arithmetic/_3E b) l1 /\ h4/list/EVERY (h4/arithmetic/_3E b) l2 ==> (h4/numposrep/l2n b (h4/list/APPEND l1 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/list/NIL)) = h4/numposrep/l2n b (h4/list/APPEND l2 (h4/list/CONS (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/list/NIL)) <=> l1 = l2)
% Assm [h4s_patriciau_u_castss_EVERYu_u_MAPu_u_ORD]: !l. h4/list/EVERY (h4/arithmetic/_3E (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)))))))))) (h4/list/MAP h4/string/ORD l)
% Assm [h4s_patriciau_u_castss_MAPu_u_11]: !l2 l1 f. (!x y. happ f x = happ f y <=> x = y) ==> (h4/list/MAP f l1 = h4/list/MAP f l2 <=> l1 = l2)
% Assm [h4s_patriciau_u_castss_REVERSEu_u_11]: !l2 l1. h4/list/REVERSE l1 = h4/list/REVERSE l2 <=> l1 = l2
% Goal: !t s. h4/patricia__casts/string__to__num s = h4/patricia__casts/string__to__num t <=> s = t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q205014,TV_Q205010]: ![V_f, V_g]: (![V_x]: s(TV_Q205010,happ(s(t_fun(TV_Q205014,TV_Q205010),V_f),s(TV_Q205014,V_x))) = s(TV_Q205010,happ(s(t_fun(TV_Q205014,TV_Q205010),V_g),s(TV_Q205014,V_x))) => s(t_fun(TV_Q205014,TV_Q205010),V_f) = s(t_fun(TV_Q205014,TV_Q205010),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> 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_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_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAPu_u_APPEND, axiom, ![TV_u_27b,TV_u_27a]: ![V_l2, V_l1, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_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_27b),h4s_lists_append(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_l1))),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_l2)))))).
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),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),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_strings_ORDu_u_11, axiom, ![V_au_27, V_a]: (s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_strings_char,V_a))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_strings_char,V_au_27))) <=> s(t_h4s_strings_char,V_a) = s(t_h4s_strings_char,V_au_27))).
fof(ah4s_strings_ORDu_u_CHRu_u_RWT, axiom, ![V_r]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_r),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)))))))))))))))))))))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_ASCIInumberss_s2nu_u_def, axiom, ![V_s, V_f, V_b]: s(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_patriciau_u_castss_stringu_u_tou_u_numu_u_def, axiom, ![V_s]: s(t_h4s_nums_num,h4s_patriciau_u_castss_stringu_u_tou_u_num(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(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_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))))))))))))))))))),s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_cons(s(t_h4s_strings_char,h4s_strings_chr(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_lists_list(t_h4s_strings_char),V_s)))))).
fof(ah4s_patriciau_u_castss_l2nu_u_11, axiom, ![V_l2, V_l1, 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_l1)))) & 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_l2)))))) => (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_append(s(t_h4s_lists_list(t_h4s_nums_num),V_l1),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(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_lists_list(t_h4s_nums_num),h4s_lists_nil))))))) = 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_append(s(t_h4s_lists_list(t_h4s_nums_num),V_l2),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(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_lists_list(t_h4s_nums_num),h4s_lists_nil))))))) <=> s(t_h4s_lists_list(t_h4s_nums_num),V_l1) = s(t_h4s_lists_list(t_h4s_nums_num),V_l2)))).
fof(ah4s_patriciau_u_castss_EVERYu_u_MAPu_u_ORD, axiom, ![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,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))))))))))))))))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(t_h4s_strings_char,t_h4s_nums_num),h4s_strings_ord),s(t_h4s_lists_list(t_h4s_strings_char),V_l))))))).
fof(ah4s_patriciau_u_castss_MAPu_u_11, axiom, ![TV_u_27b,TV_u_27a]: ![V_l2, V_l1, V_f]: (![V_x, V_y]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) => (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_l1))) = 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_l2))) <=> s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l2)))).
fof(ah4s_patriciau_u_castss_REVERSEu_u_11, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l2))) <=> s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l2))).
fof(ch4s_patriciau_u_castss_stringu_u_tou_u_numu_u_11, conjecture, ![V_t, V_s]: (s(t_h4s_nums_num,h4s_patriciau_u_castss_stringu_u_tou_u_num(s(t_h4s_lists_list(t_h4s_strings_char),V_s))) = s(t_h4s_nums_num,h4s_patriciau_u_castss_stringu_u_tou_u_num(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),V_t))).
