# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag),file('i/f/bag/SET__OF__EMPTY', ch4s_bags_SETu_u_OFu_u_EMPTY)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/SET__OF__EMPTY', aHLu_FALSITY)).
fof(5, 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/SET__OF__EMPTY', aHLu_EXT)).
fof(7, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/bag/SET__OF__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, 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/SET__OF__EMPTY', ah4s_bags_EMPTYu_u_BAG0)).
fof(15, axiom,![X11]:![X1]:![X10]:![X7]:s(X1,happ(s(t_fun(X11,X1),h4s_combins_k(s(X1,X7))),s(X11,X10)))=s(X1,X7),file('i/f/bag/SET__OF__EMPTY', ah4s_combins_Ku_u_THM)).
fof(16, axiom,![X1]:![X7]:~(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/bag/SET__OF__EMPTY', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(17, axiom,![X1]:![X13]:![X7]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(X1,t_bool),X13))),s(X1,X7)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X13))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/SET__OF__EMPTY', ah4s_bags_BAGu_u_OFu_u_SET0)).
fof(19, axiom,![X1]:![X8]:![X9]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X9),s(X1,X8)))=s(X1,X8),file('i/f/bag/SET__OF__EMPTY', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
# SZS output end CNFRefutation
