%   ORIGINAL: h4/relation/RSUBSET__antisymmetric
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/relation/antisymmetric__def: !R. h4/relation/antisymmetric R <=> (!x y. R x y /\ R y x ==> x = y)
% Assm: h4/relation/RSUBSET__ANTISYM: !R2 R1. h4/relation/RSUBSET R1 R2 /\ h4/relation/RSUBSET R2 R1 ==> R1 = R2
% Goal: h4/relation/antisymmetric h4/relation/RSUBSET
%   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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_relations_antisymmetricu_u_def]: !R. h4/relation/antisymmetric R <=> (!x y. happ (happ R x) y /\ happ (happ R y) x ==> x = y)
% Assm [h4s_relations_RSUBSETu_u_ANTISYM]: !R2 R1. happ (happ h4/relation/RSUBSET R1) R2 /\ happ (happ h4/relation/RSUBSET R2) R1 ==> R1 = R2
% Goal: h4/relation/antisymmetric h4/relation/RSUBSET
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_Q265432,TV_Q265428]: ![V_f, V_g]: (![V_x]: s(TV_Q265428,happ(s(t_fun(TV_Q265432,TV_Q265428),V_f),s(TV_Q265432,V_x))) = s(TV_Q265428,happ(s(t_fun(TV_Q265432,TV_Q265428),V_g),s(TV_Q265432,V_x))) => s(t_fun(TV_Q265432,TV_Q265428),V_f) = s(t_fun(TV_Q265432,TV_Q265428),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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_relations_antisymmetricu_u_def, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> ![V_x, 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)))) & 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_y))),s(TV_u_27a,V_x))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_relations_RSUBSETu_u_ANTISYM, axiom, ![TV_u_27a,TV_u_27b]: ![V_R2, V_R1]: ((p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R2)))) & p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R2))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R1))))) => s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R1) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R2))).
fof(ch4s_relations_RSUBSETu_u_antisymmetric, conjecture, ![TV_u_27a,TV_u_27b]: p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_bool)),h4s_relations_rsubset))))).
