%   ORIGINAL: 'h4/thm/pred_set/INFINITE_UNIV_'
% 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
% Goal: ~'h4/const/pred_set/FINITE' 'h4/const/pred_set/UNIV' <=> (?f. (!x y. f x = f y ==> x = y) /\ (?y. !x. ~(f x = y)))
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: ~'h4/const/pred_set/FINITE' 'h4/const/pred_set/UNIV' <=> (?f. (!x y. happ f x = happ f y ==> x = y) /\ (?y. !x. ~(happ f x = y)))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f20196,V_3f20192]: ![F, G]: (![X]: s(V_3f20192,happ(s(fun(V_3f20196,V_3f20192),F),s(V_3f20196,X))) = s(V_3f20192,happ(s(fun(V_3f20196,V_3f20192),G),s(V_3f20196,X))) => s(fun(V_3f20196,V_3f20192),F) = s(fun(V_3f20196,V_3f20192),G))).
fof('h4/thm/pred_set/INFINITE_UNIV_', conjecture, ![A]: (~ (p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),'h4/const/pred_set/UNIV'))))) <=> ?[F]: (![X, Y]: (s(A,happ(s(fun(A,A),F),s(A,X))) = s(A,happ(s(fun(A,A),F),s(A,Y))) => s(A,X) = s(A,Y)) & ?[Y]: ![X]: ~ (s(A,happ(s(fun(A,A),F),s(A,X))) = s(A,Y))))).
