# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X2),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(X2,t_bool),X3))))<=>s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/SURJ__EMPTY_c0', ch4s_predu_u_sets_SURJu_u_EMPTYu_c0)).
fof(3, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(45, axiom,![X1]:![X2]:![X3]:![X4]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X2),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(X2,t_bool),X3)))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_predu_u_sets_INJu_u_EMPTYu_c0)).
fof(48, axiom,![X1]:![X2]:![X4]:s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_predu_u_sets_IMAGEu_u_EMPTY)).
fof(49, axiom,![X1]:![X8]:~(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(54, axiom,![X1]:![X11]:![X3]:(s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),X11)<=>![X8]:s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X11)))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_predu_u_sets_EXTENSION)).
fof(55, axiom,![X1]:![X8]:![X26]:s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X26)))=s(t_bool,happ(s(t_fun(X1,t_bool),X26),s(X1,X8))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_bools_INu_u_DEF)).
fof(56, axiom,~(p(s(t_bool,f0))),file('i/f/pred_set/SURJ__EMPTY_c0', aHLu_FALSITY)).
fof(59, axiom,![X11]:(s(t_bool,X11)=s(t_bool,f0)<=>~(p(s(t_bool,X11)))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(67, axiom,(p(s(t_bool,f0))<=>![X11]:p(s(t_bool,X11))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_bools_Fu_u_DEF)).
fof(71, axiom,![X1]:![X2]:![X11]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X2),X4),s(t_fun(X1,t_bool),X3),s(t_fun(X2,t_bool),X11))))<=>(![X8]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X3))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X8))),s(t_fun(X2,t_bool),X11)))))&![X8]:(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X11))))=>?[X12]:(p(s(t_bool,h4s_bools_in(s(X1,X12),s(t_fun(X1,t_bool),X3))))&s(X2,happ(s(t_fun(X1,X2),X4),s(X1,X12)))=s(X2,X8))))),file('i/f/pred_set/SURJ__EMPTY_c0', ah4s_predu_u_sets_SURJu_u_DEF)).
# SZS output end CNFRefutation
