# 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),X5))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))=>p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X4),s(t_h4s_nums_num,X3),s(t_fun(X1,t_h4s_nums_num),X5))))),file('i/f/bag/BAG__INN__LESS', ch4s_bags_BAGu_u_INNu_u_LESS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__INN__LESS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__INN__LESS', aHLu_FALSITY)).
fof(9, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/bag/BAG__INN__LESS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/bag/BAG__INN__LESS', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(15, axiom,![X16]:![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),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,X16)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X16))))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(17, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_ADDu_u_SYM)).
fof(19, axiom,![X16]:![X2]:![X3]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X16))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(20, axiom,![X1]:![X2]:![X4]:![X5]: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(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X5),s(X1,X4))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__LESS', ah4s_bags_BAGu_u_INN0)).
fof(22, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/bag/BAG__INN__LESS', aHLu_BOOLu_CASES)).
fof(23, axiom,![X2]:![X3]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),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,X3))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_LESSu_u_EQ)).
fof(25, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(26, axiom,![X2]:![X3]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_GREATERu_u_EQ)).
fof(27, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X3),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,X3))),s(t_h4s_nums_num,X2))))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
fof(29, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,X3),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(30, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X2))),file('i/f/bag/BAG__INN__LESS', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
# SZS output end CNFRefutation
