# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_union(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),X2),file('i/f/bag/BAG__UNION__EMPTY_c0', ch4s_bags_BAGu_u_UNIONu_u_EMPTYu_c0)).
fof(2, axiom,![X3]:![X4]:![X5]:![X6]:(![X7]:s(X4,happ(s(t_fun(X3,X4),X5),s(X3,X7)))=s(X4,happ(s(t_fun(X3,X4),X6),s(X3,X7)))=>s(t_fun(X3,X4),X5)=s(t_fun(X3,X4),X6)),file('i/f/bag/BAG__UNION__EMPTY_c0', aHLu_EXT)).
fof(4, axiom,![X1]:![X9]:![X2]:![X7]: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),X2),s(t_fun(X1,t_h4s_nums_num),X9))),s(X1,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X2),s(X1,X7))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X9),s(X1,X7))))),file('i/f/bag/BAG__UNION__EMPTY_c0', ah4s_bags_BAGu_u_UNION0)).
fof(5, axiom,![X1]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X1,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__UNION__EMPTY_c0', ah4s_bags_EMPTYu_u_BAG0)).
fof(6, axiom,![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X10),file('i/f/bag/BAG__UNION__EMPTY_c0', ah4s_arithmetics_ADDu_u_0)).
fof(7, axiom,![X8]:![X1]:![X11]:![X7]:s(X1,happ(s(t_fun(X8,X1),h4s_combins_k(s(X1,X7))),s(X8,X11)))=s(X1,X7),file('i/f/bag/BAG__UNION__EMPTY_c0', ah4s_combins_Ku_u_THM)).
# SZS output end CNFRefutation
