%   ORIGINAL: 'h4/thm/sat/dc_cond_'
% 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: !s r q p. (p <=> 'h4/const/bool/COND' q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~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: !s r q p. (p <=> 'h4/const/bool/COND' q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~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_3f67061,V_3f67057]: ![F, G]: (![X]: s(V_3f67057,happ(s(fun(V_3f67061,V_3f67057),F),s(V_3f67061,X))) = s(V_3f67057,happ(s(fun(V_3f67061,V_3f67057),G),s(V_3f67061,X))) => s(fun(V_3f67061,V_3f67057),F) = s(fun(V_3f67061,V_3f67057),G))).
fof('h4/thm/sat/dc_cond_', conjecture, ![S, R, Q, P]: (s(bool,P) = s(bool,'h4/const/bool/COND'(s(bool,Q),s(bool,R),s(bool,S))) <=> ((p(s(bool,P)) | (p(s(bool,Q)) | ~ (p(s(bool,S))))) & ((p(s(bool,P)) | (~ (p(s(bool,R))) | ~ (p(s(bool,Q))))) & ((p(s(bool,P)) | (~ (p(s(bool,R))) | ~ (p(s(bool,S))))) & ((~ (p(s(bool,Q))) | (p(s(bool,R)) | ~ (p(s(bool,P))))) & (p(s(bool,Q)) | (p(s(bool,S)) | ~ (p(s(bool,P))))))))))).
