%   ORIGINAL: 'h4/thm/relation/RTC_RTC_'
% 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/RTC' R x y ==> (!z. 'h4/const/relation/RTC' R y z ==> 'h4/const/relation/RTC' R 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/RTC' R x y ==> (!z. 'h4/const/relation/RTC' R y z ==> 'h4/const/relation/RTC' R 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_3f25778,V_3f25774]: ![F, G]: (![X]: s(V_3f25774,happ(s(fun(V_3f25778,V_3f25774),F),s(V_3f25778,X))) = s(V_3f25774,happ(s(fun(V_3f25778,V_3f25774),G),s(V_3f25778,X))) => s(fun(V_3f25778,V_3f25774),F) = s(fun(V_3f25778,V_3f25774),G))).
fof('h4/thm/relation/RTC_RTC_', conjecture, ![A]: ![R, X, Y]: (p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Y)))) => ![Z]: (p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,Y),s(A,Z)))) => p(s(bool,'h4/const/relation/RTC'(s(fun(A,fun(A,bool)),R),s(A,X),s(A,Z))))))).
