# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))),s(t_fun(X1,t_h4s_nums_num),X2))))=>(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X2))))&p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2)))))),file('i/f/bag/SUB__BAG__UNION__down', ch4s_bags_SUBu_u_BAGu_u_UNIONu_u_down)).
fof(9, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))<=>![X6]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X6))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X6))))))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
fof(11, axiom,![X1]:![X19]:![X20]:![X6]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X20),s(t_fun(X1,t_h4s_nums_num),X19))),s(X1,X6)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X20),s(X1,X6))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X19),s(X1,X6))))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_bags_BAGu_u_UNION0)).
fof(12, axiom,![X21]:![X22]:![X23]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X21))))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(13, axiom,![X21]:![X22]:![X23]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X21)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(14, axiom,![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,X23),file('i/f/bag/SUB__BAG__UNION__down', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(15, axiom,![X22]:![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X23))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_arithmetics_ADDu_u_SYM)).
fof(16, axiom,![X22]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X22)))),file('i/f/bag/SUB__BAG__UNION__down', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
