%   ORIGINAL: h4/combin/I__THM
% 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/combin/I__DEF: h4/combin/I = h4/combin/S h4/combin/K h4/combin/K
% Assm: h4/combin/K__THM: !y x. h4/combin/K x y = x
% Assm: h4/combin/S__THM: !x g f. h4/combin/S f g x = f x (g x)
% Goal: !x. h4/combin/I x = x
%   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_combins_Iu_u_DEF]: h4/combin/I = h4/combin/S h4/combin/K h4/combin/K
% Assm [h4s_combins_Ku_u_THM]: !y x. happ (happ h4/combin/K x) y = x
% Assm [h4s_combins_Su_u_THM]: !x g f. happ (h4/combin/S f g) x = happ (happ f x) (happ g x)
% Goal: !x. happ h4/combin/I x = x
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_Q221718,TV_Q221714]: ![V_f, V_g]: (![V_x]: s(TV_Q221714,happ(s(t_fun(TV_Q221718,TV_Q221714),V_f),s(TV_Q221718,V_x))) = s(TV_Q221714,happ(s(t_fun(TV_Q221718,TV_Q221714),V_g),s(TV_Q221718,V_x))) => s(t_fun(TV_Q221718,TV_Q221714),V_f) = s(t_fun(TV_Q221718,TV_Q221714),V_g))).
fof(ah4s_combins_Iu_u_DEF, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i) = s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27a),TV_u_27a)),h4s_combins_k),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_combins_k)))).
fof(ah4s_combins_Ku_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),h4s_combins_k),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(TV_u_27a,V_x)).
fof(ah4s_combins_Su_u_THM, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_x, V_g, V_f]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),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(ch4s_combins_Iu_u_THM, conjecture, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
