# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X2,t_bool),X3))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X2,t_bool),X3))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X4)))))))=>~(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X2),X5),s(t_fun(X1,t_bool),X4),s(t_fun(X2,t_bool),X3)))))),file('i/f/pred_set/PHP', ch4s_predu_u_sets_PHP)).
fof(5, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/pred_set/PHP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(34, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X2),X5),s(t_fun(X1,t_bool),X4),s(t_fun(X2,t_bool),X3))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X2,t_bool),X3)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X4))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X2,t_bool),X3))))))),file('i/f/pred_set/PHP', ah4s_predu_u_sets_INJu_u_CARD)).
fof(36, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X2),X5),s(t_fun(X1,t_bool),X4),s(t_fun(X2,t_bool),X3))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X2,t_bool),X3)))))=>p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X4))))),file('i/f/pred_set/PHP', ah4s_predu_u_sets_FINITEu_u_INJ)).
fof(48, axiom,![X30]:![X31]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,X30)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X31))),s(t_h4s_nums_num,X30))),file('i/f/pred_set/PHP', ah4s_arithmetics_LESSu_u_EQ)).
fof(61, axiom,![X30]:![X31]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X31),s(t_h4s_nums_num,X30)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X30))),s(t_h4s_nums_num,X31))))),file('i/f/pred_set/PHP', ah4s_arithmetics_NOTu_u_LEQ)).
# SZS output end CNFRefutation
