%   ORIGINAL: h4/bool/BOOL__EQ__DISTINCT_c0
% 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/T__DEF: T <=> (\x. x) = (\x. x)
% Goal: ~(T <=> F)
%   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_Tu_u_DEF]: T <=> (!x. x <=> x)
% Goal: ~(T <=> F)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q291264,TV_Q291260]: ![V_f, V_g]: (![V_x]: s(TV_Q291260,happ(s(t_fun(TV_Q291264,TV_Q291260),V_f),s(TV_Q291264,V_x))) = s(TV_Q291260,happ(s(t_fun(TV_Q291264,TV_Q291260),V_g),s(TV_Q291264,V_x))) => s(t_fun(TV_Q291264,TV_Q291260),V_f) = s(t_fun(TV_Q291264,TV_Q291260),V_g))).
fof(ah4s_bools_Tu_u_DEF, axiom, (p(s(t_bool,t)) <=> ![V_x]: s(t_bool,V_x) = s(t_bool,V_x))).
fof(ch4s_bools_BOOLu_u_EQu_u_DISTINCTu_c0, conjecture, ~ (s(t_bool,t) = s(t_bool,f))).
