%   ORIGINAL: h4/bool/IMP__F
% 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
% Assm: h4/bool/NOT__DEF: $not = (\t. t ==> F)
% Goal: !t. (t ==> F) ==> ~t
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_NOTu_u_DEF]: !x. $not x <=> x ==> F
% Goal: !t. (t ==> F) ==> ~t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q290539,TV_Q290535]: ![V_f, V_g]: (![V_x]: s(TV_Q290535,happ(s(t_fun(TV_Q290539,TV_Q290535),V_f),s(TV_Q290539,V_x))) = s(TV_Q290535,happ(s(t_fun(TV_Q290539,TV_Q290535),V_g),s(TV_Q290539,V_x))) => s(t_fun(TV_Q290539,TV_Q290535),V_f) = s(t_fun(TV_Q290539,TV_Q290535),V_g))).
fof(ah4s_bools_NOTu_u_DEF, axiom, ![V_x]: (p(s(t_bool,d_not(s(t_bool,V_x)))) <=> (p(s(t_bool,V_x)) => p(s(t_bool,f))))).
fof(ch4s_bools_IMPu_u_F, conjecture, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
