# 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),h4s_bags_emptyu_u_bag),s(t_fun(X1,t_h4s_nums_num),X2)))),file('i/f/bag/SUB__BAG__EMPTY_c0', ch4s_bags_SUBu_u_BAGu_u_EMPTYu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/SUB__BAG__EMPTY_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/SUB__BAG__EMPTY_c0', aHLu_FALSITY)).
fof(9, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/bag/SUB__BAG__EMPTY_c0', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(11, axiom,![X6]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6)))),file('i/f/bag/SUB__BAG__EMPTY_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/bag/SUB__BAG__EMPTY_c0', aHLu_BOOLu_CASES)).
fof(13, axiom,![X1]:![X8]:![X9]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X9),s(t_fun(X1,t_h4s_nums_num),X8))))<=>![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X9),s(X1,X4))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X8),s(X1,X4))))))),file('i/f/bag/SUB__BAG__EMPTY_c0', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
fof(15, axiom,![X14]:![X1]:![X15]:![X4]:s(X1,happ(s(t_fun(X14,X1),h4s_combins_k(s(X1,X4))),s(X14,X15)))=s(X1,X4),file('i/f/bag/SUB__BAG__EMPTY_c0', ah4s_combins_Ku_u_THM)).
fof(16, 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_c0', ah4s_bags_EMPTYu_u_BAG0)).
# SZS output end CNFRefutation
