%   ORIGINAL: h4/patricia__casts/num__to__string__string__to__num
% 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/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/pred__set/IN__UNIV: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm: h4/pred__set/IMAGE__IN: !x s. h4/bool/IN x s ==> (!f. h4/bool/IN (f x) (h4/pred__set/IMAGE f s))
% Assm: h4/patricia__casts/string__to__num__11: !t s. h4/patricia__casts/string__to__num s = h4/patricia__casts/string__to__num t <=> s = t
% Assm: h4/patricia__casts/string__to__num__num__to__string: !n. h4/bool/IN n (h4/pred__set/IMAGE h4/patricia__casts/string__to__num h4/pred__set/UNIV) ==> h4/patricia__casts/string__to__num (h4/patricia__casts/num__to__string n) = n
% Goal: !s. h4/patricia__casts/num__to__string (h4/patricia__casts/string__to__num s) = 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_bools_TRUTH]: 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_predu_u_sets_INu_u_UNIV]: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm [h4s_predu_u_sets_IMAGEu_u_IN]: !x s. h4/bool/IN x s ==> (!f. h4/bool/IN (happ f x) (h4/pred__set/IMAGE f s))
% Assm [h4s_patriciau_u_castss_stringu_u_tou_u_numu_u_11]: !t s. happ h4/patricia__casts/string__to__num s = happ h4/patricia__casts/string__to__num t <=> s = t
% Assm [h4s_patriciau_u_castss_stringu_u_tou_u_numu_u_numu_u_tou_u_string]: !n. h4/bool/IN n (h4/pred__set/IMAGE h4/patricia__casts/string__to__num h4/pred__set/UNIV) ==> happ h4/patricia__casts/string__to__num (h4/patricia__casts/num__to__string n) = n
% Goal: !s. h4/patricia__casts/num__to__string (happ h4/patricia__casts/string__to__num s) = s
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q205097,TV_Q205093]: ![V_f, V_g]: (![V_x]: s(TV_Q205093,happ(s(t_fun(TV_Q205097,TV_Q205093),V_f),s(TV_Q205097,V_x))) = s(TV_Q205093,happ(s(t_fun(TV_Q205097,TV_Q205093),V_g),s(TV_Q205097,V_x))) => s(t_fun(TV_Q205097,TV_Q205093),V_f) = s(t_fun(TV_Q205097,TV_Q205093),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_predu_u_sets_INu_u_UNIV, axiom, ![TV_u_27a]: ![V_x]: p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))))).
fof(ah4s_predu_u_sets_IMAGEu_u_IN, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => ![V_f]: p(s(t_bool,h4s_bools_in(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s)))))))).
fof(ah4s_patriciau_u_castss_stringu_u_tou_u_numu_u_11, axiom, ![V_t, V_s]: (s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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))).
fof(ah4s_patriciau_u_castss_stringu_u_tou_u_numu_u_numu_u_tou_u_string, axiom, ![V_n]: (p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,V_n),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_patriciau_u_castss_stringu_u_tou_u_num),s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_bool),h4s_predu_u_sets_univ)))))) => s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),t_h4s_nums_num),h4s_patriciau_u_castss_stringu_u_tou_u_num),s(t_h4s_lists_list(t_h4s_strings_char),h4s_patriciau_u_castss_numu_u_tou_u_string(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n))).
fof(ch4s_patriciau_u_castss_numu_u_tou_u_stringu_u_stringu_u_tou_u_num, conjecture, ![V_s]: s(t_h4s_lists_list(t_h4s_strings_char),h4s_patriciau_u_castss_numu_u_tou_u_string(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_strings_char),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_lists_list(t_h4s_strings_char),V_s)).
