%   ORIGINAL: h4/integer__word/INT__ZERO__LE__INT__MAX
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/integer/INT__LE: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/words/ZERO__LE__INT__MAX: h4/arithmetic/_3C_3D h4/num/0 (h4/words/INT__MAX h4/bool/the__value)
% Assm: h4/integer__word/INT__MAX0: h4/integer__word/INT__MAX h4/bool/the__value = h4/integer/int__of__num (h4/words/INT__MAX h4/bool/the__value)
% Goal: h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer__word/INT__MAX h4/bool/the__value)
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_integers_INTu_u_LE]: !n m. h4/integer/int__le (h4/integer/int__of__num m) (h4/integer/int__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_wordss_ZEROu_u_LEu_u_INTu_u_MAX]: h4/arithmetic/_3C_3D h4/num/0 (h4/words/INT__MAX h4/bool/the__value)
% Assm [h4s_integeru_u_words_INTu_u_MAX0]: h4/integer__word/INT__MAX h4/bool/the__value = h4/integer/int__of__num (h4/words/INT__MAX h4/bool/the__value)
% Goal: h4/integer/int__le (h4/integer/int__of__num h4/num/0) (h4/integer__word/INT__MAX h4/bool/the__value)
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_Q298415,TV_Q298411]: ![V_f, V_g]: (![V_x]: s(TV_Q298411,happ(s(t_fun(TV_Q298415,TV_Q298411),V_f),s(TV_Q298415,V_x))) = s(TV_Q298411,happ(s(t_fun(TV_Q298415,TV_Q298411),V_g),s(TV_Q298415,V_x))) => s(t_fun(TV_Q298415,TV_Q298411),V_f) = s(t_fun(TV_Q298415,TV_Q298411),V_g))).
fof(ah4s_bools_TRUTH, axiom, 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_integers_INTu_u_LE, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_wordss_ZEROu_u_LEu_u_INTu_u_MAX, axiom, ![TV_u_27a]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_integeru_u_words_INTu_u_MAX0, axiom, ![TV_u_27a]: s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ch4s_integeru_u_words_INTu_u_ZEROu_u_LEu_u_INTu_u_MAX, conjecture, ![TV_u_27a]: p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
