%   ORIGINAL: h4/fcp/fcp__Axiom
% 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__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/fcp/cart__tybij_c0: !a. h4/fcp/mk__cart (h4/fcp/dest__cart a) = a
% Assm: h4/fcp/cart__tybij_c1: !r. (\f. T) r <=> h4/fcp/dest__cart (h4/fcp/mk__cart r) = r
% Goal: !f. ?g. !h. g (h4/fcp/mk__cart h) = f h
%   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_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_combins_ou_u_THM]: !x g f. h4/combin/o f g x = happ f (happ g x)
% Assm [h4s_fcps_cartu_u_tybiju_c0]: !a. h4/fcp/mk__cart (h4/fcp/dest__cart a) = a
% Assm [h4s_fcps_cartu_u_tybiju_c1]: !r. T <=> h4/fcp/dest__cart (h4/fcp/mk__cart r) = r
% Goal: !f. ?g. !h. happ g (h4/fcp/mk__cart h) = happ f h
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q190023,TV_Q190019]: ![V_f, V_g]: (![V_x]: s(TV_Q190019,happ(s(t_fun(TV_Q190023,TV_Q190019),V_f),s(TV_Q190023,V_x))) = s(TV_Q190019,happ(s(t_fun(TV_Q190023,TV_Q190019),V_g),s(TV_Q190023,V_x))) => s(t_fun(TV_Q190023,TV_Q190019),V_f) = s(t_fun(TV_Q190023,TV_Q190019),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_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_fcps_cartu_u_tybiju_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_a]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_mku_u_cart(s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),h4s_fcps_destu_u_cart(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_a))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_a)).
fof(ah4s_fcps_cartu_u_tybiju_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_r]: (p(s(t_bool,t)) <=> s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),h4s_fcps_destu_u_cart(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_mku_u_cart(s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),V_r))))) = s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),V_r))).
fof(ch4s_fcps_fcpu_u_Axiom, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_f]: ?[V_g]: ![V_h]: s(TV_u_27c,happ(s(t_fun(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),TV_u_27c),V_g),s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_mku_u_cart(s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),V_h))))) = s(TV_u_27c,happ(s(t_fun(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),TV_u_27c),V_f),s(t_fun(t_h4s_fcps_finiteu_u_image(TV_u_27b),TV_u_27a),V_h)))).
