# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)<=>(s(t_fun(X1,t_h4s_nums_num),X3)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)&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/BAG__UNION__EMPTY_c2', ch4s_bags_BAGu_u_UNIONu_u_EMPTYu_c2)).
fof(19, axiom,![X7]:s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X7,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__UNION__EMPTY_c2', ah4s_bags_EMPTYu_u_BAG0)).
fof(20, axiom,![X14]:![X15]:![X16]:![X17]:(![X8]:s(X15,happ(s(t_fun(X14,X15),X16),s(X14,X8)))=s(X15,happ(s(t_fun(X14,X15),X17),s(X14,X8)))=>s(t_fun(X14,X15),X16)=s(t_fun(X14,X15),X17)),file('i/f/bag/BAG__UNION__EMPTY_c2', aHLu_EXT)).
fof(22, axiom,![X18]:![X7]:![X19]:![X8]:s(X7,happ(s(t_fun(X18,X7),h4s_combins_k(s(X7,X8))),s(X18,X19)))=s(X7,X8),file('i/f/bag/BAG__UNION__EMPTY_c2', ah4s_combins_Ku_u_THM)).
fof(23, axiom,![X7]:![X20]:![X21]:![X8]:s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X7,t_h4s_nums_num),X21),s(t_fun(X7,t_h4s_nums_num),X20))),s(X7,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X21),s(X7,X8))),s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X20),s(X7,X8))))),file('i/f/bag/BAG__UNION__EMPTY_c2', ah4s_bags_BAGu_u_UNION0)).
fof(24, 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_nums_0)<=>(s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__UNION__EMPTY_c2', ah4s_arithmetics_ADDu_u_EQu_u_0)).
# SZS output end CNFRefutation
