%   ORIGINAL: 'h4/thm/relation/TC_implies_one_step_'
% 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: !R x y. 'h4/const/relation/TC' R x y /\ ~(x = y) ==> (?z. R x z /\ ~(x = z))
%   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: !R x y. 'h4/const/relation/TC' R x y /\ ~(x = y) ==> (?z. happ (happ R x) z /\ ~(x = z))
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_3f26553,V_3f26549]: ![F, G]: (![X]: s(V_3f26549,happ(s(fun(V_3f26553,V_3f26549),F),s(V_3f26553,X))) = s(V_3f26549,happ(s(fun(V_3f26553,V_3f26549),G),s(V_3f26553,X))) => s(fun(V_3f26553,V_3f26549),F) = s(fun(V_3f26553,V_3f26549),G))).
fof('h4/thm/relation/TC_implies_one_step_', conjecture, ![A]: ![R, X, Y]: ((p(s(bool,'h4/const/relation/TC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Y)))) & ~ (s(A,X) = s(A,Y))) => ?[Z]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),R),s(A,X))),s(A,Z)))) & ~ (s(A,X) = s(A,Z))))).
