%   ORIGINAL: 'h4/thm/sat/dc_eq_'
% 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 q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
%   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 q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
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_3f66936,V_3f66932]: ![F, G]: (![X]: s(V_3f66932,happ(s(fun(V_3f66936,V_3f66932),F),s(V_3f66936,X))) = s(V_3f66932,happ(s(fun(V_3f66936,V_3f66932),G),s(V_3f66936,X))) => s(fun(V_3f66936,V_3f66932),F) = s(fun(V_3f66936,V_3f66932),G))).
fof('h4/thm/sat/dc_eq_', conjecture, ![R, Q, P]: ((p(s(bool,P)) <=> s(bool,Q) = s(bool,R)) <=> ((p(s(bool,P)) | (p(s(bool,Q)) | p(s(bool,R)))) & ((p(s(bool,P)) | (~ (p(s(bool,R))) | ~ (p(s(bool,Q))))) & ((p(s(bool,Q)) | (~ (p(s(bool,R))) | ~ (p(s(bool,P))))) & (p(s(bool,R)) | (~ (p(s(bool,Q))) | ~ (p(s(bool,P)))))))))).
