# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X5))))))<=>((p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_fun(X1,t_h4s_nums_num),X5))))&s(X1,X4)=s(X1,X3))|(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X5))))&~(s(X1,X4)=s(X1,X3))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ch4s_bags_BAGu_u_INNu_u_BAGu_u_INSERTu_u_STRONG)).
fof(4, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(35, axiom,![X2]:![X22]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X2)))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_SUBu_u_LESSu_u_EQ)).
fof(36, axiom,![X2]:![X22]:(s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,X2)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X22)))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(38, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X5))))))<=>((p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_fun(X1,t_h4s_nums_num),X5))))&s(X1,X4)=s(X1,X3))|p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X5)))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_bags_BAGu_u_INNu_u_BAGu_u_INSERT)).
fof(40, axiom,![X1]:![X2]:![X22]:![X25]:![X5]:((p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X25),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X5))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X2)))))=>p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X25),s(t_h4s_nums_num,X22),s(t_fun(X1,t_h4s_nums_num),X5))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_bags_BAGu_u_INNu_u_LESS)).
fof(63, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_ONE)).
fof(65, axiom,![X15]:![X2]:![X22]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_SUBu_u_LEFTu_u_GREATERu_u_EQ)).
fof(70, axiom,![X1]:![X25]:![X5]:![X7]:?[X33]:((p(s(t_bool,X33))<=>s(X1,X7)=s(X1,X25))&s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X25),s(t_fun(X1,t_h4s_nums_num),X5))),s(X1,X7)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,X33),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X5),s(X1,X25))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X5),s(X1,X7)))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_bags_BAGu_u_INSERT0)).
fof(73, axiom,![X2]:![X22]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X2))))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(74, axiom,![X2]:![X22]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X22)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_GREATERu_u_EQ)).
fof(75, axiom,![X2]:![X22]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__BAG__INSERT__STRONG', ah4s_arithmetics_LESSu_u_EQ)).
# SZS output end CNFRefutation
