# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(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)<=>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))))),file('i/f/bag/BAG__DIFF__EQ__EMPTY', ch4s_bags_BAGu_u_DIFFu_u_EQu_u_EMPTY)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DIFF__EQ__EMPTY', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__DIFF__EQ__EMPTY', aHLu_FALSITY)).
fof(6, axiom,![X5]:![X6]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5))))),file('i/f/bag/BAG__DIFF__EQ__EMPTY', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(7, axiom,![X1]:![X7]:![X8]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X8),s(t_fun(X1,t_h4s_nums_num),X7))))<=>![X4]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X8),s(X1,X4))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X7),s(X1,X4))))))),file('i/f/bag/BAG__DIFF__EQ__EMPTY', ah4s_bags_SUBu_u_BAGu_u_LEQ)).
fof(8, axiom,![X9]:![X10]:![X11]:![X12]:(![X4]:s(X10,happ(s(t_fun(X9,X10),X11),s(X9,X4)))=s(X10,happ(s(t_fun(X9,X10),X12),s(X9,X4)))=>s(t_fun(X9,X10),X11)=s(t_fun(X9,X10),X12)),file('i/f/bag/BAG__DIFF__EQ__EMPTY', aHLu_EXT)).
fof(10, axiom,![X13]:![X1]:![X14]:![X4]:s(X1,happ(s(t_fun(X13,X1),h4s_combins_k(s(X1,X4))),s(X13,X14)))=s(X1,X4),file('i/f/bag/BAG__DIFF__EQ__EMPTY', ah4s_combins_Ku_u_THM)).
fof(11, 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/BAG__DIFF__EQ__EMPTY', ah4s_bags_EMPTYu_u_BAG0)).
fof(12, axiom,![X1]:![X7]:![X8]:![X4]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(X1,t_h4s_nums_num),X8),s(t_fun(X1,t_h4s_nums_num),X7))),s(X1,X4)))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X8),s(X1,X4))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X7),s(X1,X4))))),file('i/f/bag/BAG__DIFF__EQ__EMPTY', ah4s_bags_BAGu_u_DIFF0)).
fof(13, axiom,![X15]:(s(t_bool,X15)=s(t_bool,t)|s(t_bool,X15)=s(t_bool,f)),file('i/f/bag/BAG__DIFF__EQ__EMPTY', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
