%   ORIGINAL: h4/pred__set/NOT__IN__EMPTY
% 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/FALSITY: !t. F ==> t
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Assm: h4/pred__set/EMPTY__DEF: h4/pred__set/EMPTY = (\x. F)
% Goal: !x. ~h4/bool/IN x h4/pred__set/EMPTY
%   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_FALSITY]: !t. F ==> t
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Assm [h4s_predu_u_sets_EMPTYu_u_DEF]: !x. happ h4/pred__set/EMPTY x <=> F
% Goal: !x. ~h4/bool/IN x h4/pred__set/EMPTY
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_Q146796,TV_Q146792]: ![V_f, V_g]: (![V_x]: s(TV_Q146792,happ(s(t_fun(TV_Q146796,TV_Q146792),V_f),s(TV_Q146796,V_x))) = s(TV_Q146792,happ(s(t_fun(TV_Q146796,TV_Q146792),V_g),s(TV_Q146796,V_x))) => s(t_fun(TV_Q146796,TV_Q146792),V_f) = s(t_fun(TV_Q146796,TV_Q146792),V_g))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ah4s_predu_u_sets_EMPTYu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(TV_u_27a,V_x))) = s(t_bool,f)).
fof(ch4s_predu_u_sets_NOTu_u_INu_u_EMPTY, conjecture, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
