%   ORIGINAL: h4/util__prob/X__LE__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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/MAX__LE_c0: !p n m. h4/arithmetic/_3C_3D p (h4/arithmetic/MAX m n) <=> h4/arithmetic/_3C_3D p m \/ h4/arithmetic/_3C_3D p n
% Goal: !n m k. h4/arithmetic/_3C_3D k (h4/arithmetic/MAX m n) <=> h4/arithmetic/_3C_3D k m \/ h4/arithmetic/_3C_3D k n
%   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_arithmetics_MAXu_u_LEu_c0]: !p n m. h4/arithmetic/_3C_3D p (h4/arithmetic/MAX m n) <=> h4/arithmetic/_3C_3D p m \/ h4/arithmetic/_3C_3D p n
% Goal: !n m k. h4/arithmetic/_3C_3D k (h4/arithmetic/MAX m n) <=> h4/arithmetic/_3C_3D k m \/ h4/arithmetic/_3C_3D k n
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_Q183584,TV_Q183580]: ![V_f, V_g]: (![V_x]: s(TV_Q183580,happ(s(t_fun(TV_Q183584,TV_Q183580),V_f),s(TV_Q183584,V_x))) = s(TV_Q183580,happ(s(t_fun(TV_Q183584,TV_Q183580),V_g),s(TV_Q183584,V_x))) => s(t_fun(TV_Q183584,TV_Q183580),V_f) = s(t_fun(TV_Q183584,TV_Q183580),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_arithmetics_MAXu_u_LEu_c0, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_arithmetics_max(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_p),s(t_h4s_nums_num,V_m)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_n))))))).
fof(ch4s_utilu_u_probs_Xu_u_LEu_u_MAX, conjecture, ![V_n, V_m, V_k]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,h4s_arithmetics_max(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_k),s(t_h4s_nums_num,V_m)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))))))).
