# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_bags_subu_u_bag(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)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)),file('i/f/bag/SUB__BAG__EMPTY_c1', ch4s_bags_SUBu_u_BAGu_u_EMPTYu_c1)).
fof(42, axiom,![X1]:![X4]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag),s(X1,X4)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_bags_EMPTYu_u_BAGu_u_alt)).
fof(43, axiom,![X26]:![X27]:![X28]:![X29]:(![X4]:s(X27,happ(s(t_fun(X26,X27),X28),s(X26,X4)))=s(X27,happ(s(t_fun(X26,X27),X29),s(X26,X4)))=>s(t_fun(X26,X27),X28)=s(t_fun(X26,X27),X29)),file('i/f/bag/SUB__BAG__EMPTY_c1', aHLu_EXT)).
fof(58, axiom,![X25]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X25)))),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(65, axiom,![X25]:![X35]:(s(t_h4s_nums_num,X35)=s(t_h4s_nums_num,X25)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X35),s(t_h4s_nums_num,X25))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X35)))))),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(81, axiom,![X1]:![X23]:![X24]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X24),s(t_fun(X1,t_h4s_nums_num),X23))))<=>![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X24),s(X1,X4))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X23),s(X1,X4))))))),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
# SZS output end CNFRefutation
