# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bag/NOT__IN__EMPTY__BAG', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/NOT__IN__EMPTY__BAG', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/bag/NOT__IN__EMPTY__BAG', aHLu_BOOLu_CASES)).
fof(8, axiom,![X8]:![X7]:![X9]:![X6]:s(X7,happ(s(t_fun(X8,X7),h4s_combins_k(s(X7,X6))),s(X8,X9)))=s(X7,X6),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_combins_Ku_u_THM)).
fof(9, axiom,![X10]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_numerals_numeralu_u_distribu_c17)).
fof(10, axiom,![X10]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))<=>s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_numerals_numeralu_u_distribu_c30)).
fof(11, axiom,![X10]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_numerals_numeralu_u_equ_c1)).
fof(12, axiom,![X7]:s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X7,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_bags_EMPTYu_u_BAG0)).
fof(13, axiom,![X7]:![X10]:![X11]:![X12]:s(t_bool,h4s_bags_bagu_u_inn(s(X7,X11),s(t_h4s_nums_num,X10),s(t_fun(X7,t_h4s_nums_num),X12)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X12),s(X7,X11))),s(t_h4s_nums_num,X10))),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_bags_BAGu_u_INN0)).
fof(14, axiom,![X7]:![X11]:![X12]:s(t_bool,h4s_bags_bagu_u_in(s(X7,X11),s(t_fun(X7,t_h4s_nums_num),X12)))=s(t_bool,h4s_bags_bagu_u_inn(s(X7,X11),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_fun(X7,t_h4s_nums_num),X12))),file('i/f/bag/NOT__IN__EMPTY__BAG', ah4s_bags_BAGu_u_IN0)).
fof(15, conjecture,![X7]:![X6]:~(p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X6),s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))),file('i/f/bag/NOT__IN__EMPTY__BAG', ch4s_bags_NOTu_u_INu_u_EMPTYu_u_BAG)).
# SZS output end CNFRefutation
