# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(?[X3]:p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X2))))<=>~(s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))),file('i/f/bag/MEMBER__NOT__EMPTY', ch4s_bags_MEMBERu_u_NOTu_u_EMPTY)).
fof(31, axiom,![X1]:![X3]:![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),X2)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)),file('i/f/bag/MEMBER__NOT__EMPTY', ah4s_bags_BAGu_u_INSERTu_u_NOTu_u_EMPTY)).
fof(34, axiom,![X1]:![X2]:(s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)|?[X22]:?[X21]:s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X22)))),file('i/f/bag/MEMBER__NOT__EMPTY', ah4s_bags_BAGu_u_cases)).
fof(37, axiom,![X1]:![X21]:![X2]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X2))))=>?[X25]:s(t_fun(X1,t_h4s_nums_num),X2)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X25)))),file('i/f/bag/MEMBER__NOT__EMPTY', ah4s_bags_BAGu_u_DECOMPOSE)).
fof(40, axiom,![X1]:![X21]:![X22]:![X2]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X22),s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X2))))=>p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X22))))),file('i/f/bag/MEMBER__NOT__EMPTY', ah4s_bags_BAGu_u_DELETEu_u_BAGu_u_IN)).
fof(41, axiom,![X1]:![X21]:![X22]:![X2]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X22),s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X2))))<=>s(t_fun(X1,t_h4s_nums_num),X22)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X21),s(t_fun(X1,t_h4s_nums_num),X2)))),file('i/f/bag/MEMBER__NOT__EMPTY', ah4s_bags_BAGu_u_DELETE0)).
# SZS output end CNFRefutation
