%   ORIGINAL: h4/relation/IDEM__TC
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/relation/TC__IDEM: !R. h4/relation/TC (h4/relation/TC R) = h4/relation/TC R
% Assm: h4/relation/IDEM0: !f. h4/relation/IDEM f <=> (!x. f (f x) = f x)
% Goal: h4/relation/IDEM h4/relation/TC
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_relations_TCu_u_IDEM]: !R. happ h4/relation/TC (happ h4/relation/TC R) = happ h4/relation/TC R
% Assm [h4s_relations_IDEM0]: !f. h4/relation/IDEM f <=> (!x. happ f (happ f x) = happ f x)
% Goal: h4/relation/IDEM h4/relation/TC
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_Q265732,TV_Q265728]: ![V_f, V_g]: (![V_x]: s(TV_Q265728,happ(s(t_fun(TV_Q265732,TV_Q265728),V_f),s(TV_Q265732,V_x))) = s(TV_Q265728,happ(s(t_fun(TV_Q265732,TV_Q265728),V_g),s(TV_Q265732,V_x))) => s(t_fun(TV_Q265732,TV_Q265728),V_f) = s(t_fun(TV_Q265732,TV_Q265728),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_TCu_u_IDEM, axiom, ![TV_u_27a]: ![V_R]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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)),V_R))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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)),V_R)))).
fof(ah4s_relations_IDEM0, axiom, ![TV_u_27z]: ![V_f]: (p(s(t_bool,h4s_relations_idem(s(t_fun(TV_u_27z,TV_u_27z),V_f)))) <=> ![V_x]: s(TV_u_27z,happ(s(t_fun(TV_u_27z,TV_u_27z),V_f),s(TV_u_27z,happ(s(t_fun(TV_u_27z,TV_u_27z),V_f),s(TV_u_27z,V_x))))) = s(TV_u_27z,happ(s(t_fun(TV_u_27z,TV_u_27z),V_f),s(TV_u_27z,V_x))))).
fof(ch4s_relations_IDEMu_u_TC, conjecture, ![TV_u_27a]: p(s(t_bool,h4s_relations_idem(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_tc))))).
