# 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),h4s_bags_emptyu_u_bag),s(t_fun(X1,t_h4s_nums_num),X2)))=s(t_fun(X1,t_h4s_nums_num),X2),file('i/f/bag/BAG__UNION__EMPTY_c1', ch4s_bags_BAGu_u_UNIONu_u_EMPTYu_c1)).
fof(3, 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_c1', aHLu_EXT)).
fof(8, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/bag/BAG__UNION__EMPTY_c1', ah4s_arithmetics_ADDu_u_SYM)).
fof(9, axiom,![X1]:![X8]:![X12]:![X7]:s(X8,happ(s(t_fun(X1,X8),h4s_combins_k(s(X8,X7))),s(X1,X12)))=s(X8,X7),file('i/f/bag/BAG__UNION__EMPTY_c1', ah4s_combins_Ku_u_THM)).
fof(10, axiom,![X8]:s(t_fun(X8,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X8,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__UNION__EMPTY_c1', ah4s_bags_EMPTYu_u_BAG0)).
fof(11, axiom,![X8]:![X13]:![X2]:![X7]:s(t_h4s_nums_num,happ(s(t_fun(X8,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(X8,t_h4s_nums_num),X2),s(t_fun(X8,t_h4s_nums_num),X13))),s(X8,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(X8,t_h4s_nums_num),X2),s(X8,X7))),s(t_h4s_nums_num,happ(s(t_fun(X8,t_h4s_nums_num),X13),s(X8,X7))))),file('i/f/bag/BAG__UNION__EMPTY_c1', ah4s_bags_BAGu_u_UNION0)).
fof(12, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/bag/BAG__UNION__EMPTY_c1', ah4s_arithmetics_ADDu_u_0)).
# SZS output end CNFRefutation
