# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2))))<=>s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)),file('i/f/pred_set/EQ__UNIV', ch4s_predu_u_sets_EQu_u_UNIV)).
fof(3, axiom,![X1]:![X3]:![X8]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X8)))=s(t_bool,happ(s(t_fun(X1,t_bool),X8),s(X1,X3))),file('i/f/pred_set/EQ__UNIV', ah4s_predu_u_sets_SPECIFICATION)).
fof(9, axiom,![X1]:![X11]:![X2]:(~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X11))<=>?[X3]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X11))))<=>~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/EQ__UNIV', ah4s_predu_u_sets_NOTu_u_EQUALu_u_SETS)).
fof(29, axiom,![X1]:![X26]:![X6]:(![X3]:(s(X1,X3)=s(X1,X26)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X3)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X26))))),file('i/f/pred_set/EQ__UNIV', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(38, axiom,![X1]:![X3]:s(t_bool,happ(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(X1,X3)))=s(t_bool,t),file('i/f/pred_set/EQ__UNIV', ah4s_predu_u_sets_UNIVu_u_DEF)).
fof(42, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/EQ__UNIV', aHLu_FALSITY)).
fof(44, axiom,![X11]:(s(t_bool,f)=s(t_bool,X11)<=>~(p(s(t_bool,X11)))),file('i/f/pred_set/EQ__UNIV', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(46, axiom,(p(s(t_bool,f))<=>![X11]:p(s(t_bool,X11))),file('i/f/pred_set/EQ__UNIV', ah4s_bools_Fu_u_DEF)).
fof(54, axiom,p(s(t_bool,t)),file('i/f/pred_set/EQ__UNIV', aHLu_TRUTH)).
fof(55, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/pred_set/EQ__UNIV', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
