%   ORIGINAL: h4/relation/EQC__REFL
% 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/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/relation/RC__DEF: !y x R. h4/relation/RC R x y <=> x = y \/ R x y
% Assm: h4/relation/EQC__DEF: !R. h4/relation/EQC R = h4/relation/RC (h4/relation/TC (h4/relation/SC R))
% Goal: !x R. h4/relation/EQC R 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_bools_TRUTH]: T
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_relations_RCu_u_DEF]: !y x R. happ (happ (h4/relation/RC R) x) y <=> x = y \/ happ (happ R x) y
% Assm [h4s_relations_EQCu_u_DEF]: !R. h4/relation/EQC R = h4/relation/RC (h4/relation/TC (h4/relation/SC R))
% Goal: !x R. happ (happ (h4/relation/EQC R) 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_Q263157,TV_Q263153]: ![V_f, V_g]: (![V_x]: s(TV_Q263153,happ(s(t_fun(TV_Q263157,TV_Q263153),V_f),s(TV_Q263157,V_x))) = s(TV_Q263153,happ(s(t_fun(TV_Q263157,TV_Q263153),V_g),s(TV_Q263157,V_x))) => s(t_fun(TV_Q263157,TV_Q263153),V_f) = s(t_fun(TV_Q263157,TV_Q263153),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> 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_relations_RCu_u_DEF, axiom, ![TV_u_27a]: ![V_y, V_x, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_rc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))))).
fof(ah4s_relations_EQCu_u_DEF, axiom, ![TV_u_27a]: ![V_R]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_eqc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_rc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_sc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))))))).
fof(ch4s_relations_EQCu_u_REFL, conjecture, ![TV_u_27a]: ![V_x, V_R]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_eqc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))),s(TV_u_27a,V_x))))).
