# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_h4s_nums_num),X2))))=>s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X1,t_h4s_nums_num),X3),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/BAG__DIFF__EMPTY_c3', ch4s_bags_BAGu_u_DIFFu_u_EMPTYu_c3)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DIFF__EMPTY_c3', aHLu_TRUTH)).
fof(3, axiom,![X4]:![X5]:![X6]:![X7]:(![X8]:s(X5,happ(s(t_fun(X4,X5),X6),s(X4,X8)))=s(X5,happ(s(t_fun(X4,X5),X7),s(X4,X8)))=>s(t_fun(X4,X5),X6)=s(t_fun(X4,X5),X7)),file('i/f/bag/BAG__DIFF__EMPTY_c3', aHLu_EXT)).
fof(9, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X9]:s(t_fun(X9,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X9,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_bags_EMPTYu_u_BAG0)).
fof(13, axiom,![X12]:![X9]:![X11]:![X8]:s(X9,happ(s(t_fun(X12,X9),h4s_combins_k(s(X9,X8))),s(X12,X11)))=s(X9,X8),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_combins_Ku_u_THM)).
fof(14, axiom,![X9]:![X2]:![X3]:![X8]:s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X9,t_h4s_nums_num),X3),s(t_fun(X9,t_h4s_nums_num),X2))),s(X9,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),X3),s(X9,X8))),s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),X2),s(X9,X8))))),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_bags_BAGu_u_DIFF0)).
fof(15, axiom,![X9]:![X2]:![X3]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X9,t_h4s_nums_num),X3),s(t_fun(X9,t_h4s_nums_num),X2))))<=>![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),X3),s(X9,X8))),s(t_h4s_nums_num,happ(s(t_fun(X9,t_h4s_nums_num),X2),s(X9,X8))))))),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
fof(16, axiom,![X18]:![X19]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))),file('i/f/bag/BAG__DIFF__EMPTY_c3', ah4s_arithmetics_SUBu_u_EQu_u_0)).
# SZS output end CNFRefutation
