# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__IN__BAG__FILTER', aHLu_TRUTH)).
fof(5, axiom,![X7]:![X8]:![X9]:![X6]:s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X7,t_bool),X9),s(t_fun(X7,t_h4s_nums_num),X8))),s(X7,X6)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X6))),s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X8),s(X7,X6))),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_FILTERu_u_DEF)).
fof(7, axiom,![X7]:![X11]:![X10]:![X8]:![X9]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X7,X10),s(t_h4s_nums_num,X11),s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X7,t_bool),X9),s(t_fun(X7,t_h4s_nums_num),X8))))))<=>(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)|(p(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X10))))&p(s(t_bool,h4s_bags_bagu_u_inn(s(X7,X10),s(t_h4s_nums_num,X11),s(t_fun(X7,t_h4s_nums_num),X8))))))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_INNu_u_BAGu_u_FILTER)).
fof(15, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X7]:![X13]:![X14]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X14),s(X7,X13)))=s(X7,X14),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(31, axiom,![X7]:![X8]:![X6]:s(t_bool,happ(s(t_fun(X7,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(X7,t_h4s_nums_num),X8))),s(X7,X6)))=s(t_bool,h4s_bags_bagu_u_in(s(X7,X6),s(t_fun(X7,t_h4s_nums_num),X8))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_SETu_u_OFu_u_BAG0)).
fof(61, axiom,![X7]:![X11]:![X10]:![X8]:s(t_bool,h4s_bags_bagu_u_inn(s(X7,X10),s(t_h4s_nums_num,X11),s(t_fun(X7,t_h4s_nums_num),X8)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X8),s(X7,X10))),s(t_h4s_nums_num,X11))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_INN0)).
fof(65, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_numerals_numeralu_u_distribu_c1)).
fof(72, axiom,![X11]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X11))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(74, axiom,![X11]:![X27]:(~(s(t_h4s_nums_num,X27)=s(t_h4s_nums_num,X11))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X27))),s(t_h4s_nums_num,X11))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X27)))))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(76, axiom,![X11]:![X27]:(s(t_h4s_nums_num,X27)=s(t_h4s_nums_num,X11)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X11))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X27)))))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(81, axiom,![X11]:![X27]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X27)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X11))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_arithmetics_GREATERu_u_EQ)).
fof(93, axiom,![X7]:![X10]:![X8]:s(t_bool,h4s_bags_bagu_u_in(s(X7,X10),s(t_fun(X7,t_h4s_nums_num),X8)))=s(t_bool,h4s_bags_bagu_u_inn(s(X7,X10),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),X8))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_IN0)).
fof(133, conjecture,![X7]:![X10]:![X8]:![X9]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X10),s(t_fun(X7,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X7,t_bool),X9),s(t_fun(X7,t_h4s_nums_num),X8))))))<=>(p(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X10))))&p(s(t_bool,h4s_bags_bagu_u_in(s(X7,X10),s(t_fun(X7,t_h4s_nums_num),X8)))))),file('i/f/bag/BAG__IN__BAG__FILTER', ch4s_bags_BAGu_u_INu_u_BAGu_u_FILTER)).
# SZS output end CNFRefutation
