%   ORIGINAL: 'h4/thm/sat/dc_imp_'
% 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) /\ (p \/ ~r) /\ (~q \/ r \/ ~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) /\ (p \/ ~r) /\ (~q \/ r \/ ~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_3f67011,V_3f67007]: ![F, G]: (![X]: s(V_3f67007,happ(s(fun(V_3f67011,V_3f67007),F),s(V_3f67011,X))) = s(V_3f67007,happ(s(fun(V_3f67011,V_3f67007),G),s(V_3f67011,X))) => s(fun(V_3f67011,V_3f67007),F) = s(fun(V_3f67011,V_3f67007),G))).
fof('h4/thm/sat/dc_imp_', conjecture, ![R, Q, P]: ((p(s(bool,P)) <=> (p(s(bool,Q)) => p(s(bool,R)))) <=> ((p(s(bool,P)) | p(s(bool,Q))) & ((p(s(bool,P)) | ~ (p(s(bool,R)))) & (~ (p(s(bool,Q))) | (p(s(bool,R)) | ~ (p(s(bool,P))))))))).
