%   ORIGINAL: h4/enumeral/NOT__IN__nt
% 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/enumeral/IN__bt__to__set_c0: !y cmp. h4/bool/IN y (h4/enumeral/ENUMERAL cmp h4/enumeral/nt) <=> F
% Goal: !y cmp. h4/bool/IN y (h4/enumeral/ENUMERAL cmp h4/enumeral/nt) <=> 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_enumerals_INu_u_btu_u_tou_u_setu_c0]: !y cmp. h4/bool/IN y (h4/enumeral/ENUMERAL cmp h4/enumeral/nt) <=> F
% Goal: !y cmp. h4/bool/IN y (h4/enumeral/ENUMERAL cmp h4/enumeral/nt) <=> 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_Q333509,TV_Q333505]: ![V_f, V_g]: (![V_x]: s(TV_Q333505,happ(s(t_fun(TV_Q333509,TV_Q333505),V_f),s(TV_Q333509,V_x))) = s(TV_Q333505,happ(s(t_fun(TV_Q333509,TV_Q333505),V_g),s(TV_Q333509,V_x))) => s(t_fun(TV_Q333509,TV_Q333505),V_f) = s(t_fun(TV_Q333509,TV_Q333505),V_g))).
fof(ah4s_enumerals_INu_u_btu_u_tou_u_setu_c0, axiom, ![TV_u_27a]: ![V_y, V_cmp]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_enumeral(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))))) = s(t_bool,f)).
fof(ch4s_enumerals_NOTu_u_INu_u_nt, conjecture, ![TV_u_27a]: ![V_y, V_cmp]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_enumeral(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))))) = s(t_bool,f)).
