%   ORIGINAL: 'h4/thm/sat/OR_DUAL_'
% 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: !B A. ~(A \/ B) ==> F <=> ~A ==> ~B ==> F
%   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: !B A. ~(A \/ B) ==> F <=> ~A ==> ~B ==> F
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_3f66761,V_3f66757]: ![F, G]: (![X]: s(V_3f66757,happ(s(fun(V_3f66761,V_3f66757),F),s(V_3f66761,X))) = s(V_3f66757,happ(s(fun(V_3f66761,V_3f66757),G),s(V_3f66761,X))) => s(fun(V_3f66761,V_3f66757),F) = s(fun(V_3f66761,V_3f66757),G))).
fof('h4/thm/sat/OR_DUAL_', conjecture, ![B, A]: ((~ ((p(s(bool,A)) | p(s(bool,B)))) => p(s(bool,'F'))) <=> (~ (p(s(bool,A))) => (~ (p(s(bool,B))) => p(s(bool,'F')))))).
