# 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(X2,X1),X4),s(t_fun(X2,t_bool),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))<=>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_c1', ch4s_predu_u_sets_SURJu_u_EMPTYu_c1)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X2]:![X8]:~(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(31, axiom,![X1]:![X2]:![X3]:![X4]:(s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),X3)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)<=>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_c1', ah4s_predu_u_sets_IMAGEu_u_EQu_u_EMPTY)).
fof(32, axiom,![X2]:![X1]:![X4]:s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_IMAGEu_u_EMPTY)).
fof(33, axiom,![X2]:![X1]:![X7]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),X3),s(t_fun(X1,t_bool),X7))))<=>(![X8]:(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X8))),s(t_fun(X1,t_bool),X7)))))&![X8]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X7))))=>?[X9]:(p(s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X3))))&s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X9)))=s(X1,X8))))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_SURJu_u_DEF)).
fof(34, axiom,![X2]:![X1]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty),s(t_fun(X1,t_bool),X3))))<=>s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_SURJu_u_EMPTYu_c0)).
fof(35, axiom,![X2]:![X19]:(![X8]:s(X2,happ(s(t_fun(X2,X2),X19),s(X2,X8)))=s(X2,X8)=>![X3]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X2,X2),X19),s(t_fun(X2,t_bool),X3),s(t_fun(X2,t_bool),X3))))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_SURJu_u_ID)).
fof(36, axiom,![X2]:![X7]:![X3]:(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),X7)<=>![X8]:s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X7)))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_EXTENSION)).
fof(37, axiom,![X2]:![X8]:![X20]:s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X20)))=s(t_bool,happ(s(t_fun(X2,t_bool),X20),s(X2,X8))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_bools_INu_u_DEF)).
fof(38, axiom,![X1]:![X2]:![X9]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X9),s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),X3))))))<=>?[X8]:(s(X1,X9)=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X8)))&p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3)))))),file('i/f/pred_set/SURJ__EMPTY_c1', ah4s_predu_u_sets_INu_u_IMAGE)).
# SZS output end CNFRefutation
