# 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(2, axiom,p(s(t_bool,t)),file('i/f/bag/SUB__BAG__EMPTY_c1', aHLu_TRUTH)).
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/SUB__BAG__EMPTY_c1', aHLu_EXT)).
fof(7, 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/SUB__BAG__EMPTY_c1', ah4s_bags_EMPTYu_u_BAG0)).
fof(8, axiom,![X8]:![X1]:![X9]:![X7]:s(X1,happ(s(t_fun(X8,X1),h4s_combins_k(s(X1,X7))),s(X8,X9)))=s(X1,X7),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_combins_Ku_u_THM)).
fof(9, axiom,![X1]:![X10]:![X11]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X11),s(t_fun(X1,t_h4s_nums_num),X10))))<=>![X7]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X11),s(X1,X7))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X10),s(X1,X7))))))),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
fof(10, axiom,![X12]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bag/SUB__BAG__EMPTY_c1', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(11, axiom,~(p(s(t_bool,f))),file('i/f/bag/SUB__BAG__EMPTY_c1', aHLu_FALSITY)).
fof(12, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)|s(t_bool,X13)=s(t_bool,f)),file('i/f/bag/SUB__BAG__EMPTY_c1', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
