%   ORIGINAL: h4/pred__set/EMPTY__applied
% 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/TRUTH: T
% Assm: h4/bool/ABS__SIMP: !t2 t1. (\x. t1) t2 = t1
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/pred__set/EMPTY__DEF: h4/pred__set/EMPTY = (\x. F)
% Goal: !x. h4/pred__set/EMPTY x <=> 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_TRUTH]: T
% Assm [h4s_bools_ABSu_u_SIMP]: !t2 t1. t1 = t1
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_predu_u_sets_EMPTYu_u_DEF]: !x. h4/pred__set/EMPTY x <=> F
% Goal: !x. h4/pred__set/EMPTY x <=> 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_Q146846,TV_Q146842]: ![V_f, V_g]: (![V_x]: s(TV_Q146842,happ(s(t_fun(TV_Q146846,TV_Q146842),V_f),s(TV_Q146846,V_x))) = s(TV_Q146842,happ(s(t_fun(TV_Q146846,TV_Q146842),V_g),s(TV_Q146846,V_x))) => s(t_fun(TV_Q146846,TV_Q146842),V_f) = s(t_fun(TV_Q146846,TV_Q146842),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ABSu_u_SIMP, axiom, ![TV_u_27b,TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,V_t1) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_predu_u_sets_EMPTYu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_predu_u_sets_empty(s(TV_u_27a,V_x))) = s(t_bool,f)).
fof(ch4s_predu_u_sets_EMPTYu_u_applied, conjecture, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_predu_u_sets_empty(s(TV_u_27a,V_x))) = s(t_bool,f)).
