# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),X3))))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X2))))&p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3)))))),file('i/f/bag/BAG__IN__BAG__FILTER', ch4s_bags_BAGu_u_INu_u_BAGu_u_FILTER)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__IN__BAG__FILTER', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__IN__BAG__FILTER', aHLu_FALSITY)).
fof(7, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_numerals_numeralu_u_equ_c1)).
fof(8, axiom,![X1]:![X7]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X2),s(t_h4s_nums_num,X7),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_h4s_nums_num),X3))))))<=>(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)|(p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X2))))&p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X2),s(t_h4s_nums_num,X7),s(t_fun(X1,t_h4s_nums_num),X3))))))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_INNu_u_BAGu_u_FILTER)).
fof(9, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/BAG__IN__BAG__FILTER', aHLu_BOOLu_CASES)).
fof(11, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3)))=s(t_bool,h4s_bags_bagu_u_inn(s(X1,X2),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(X1,t_h4s_nums_num),X3))),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_bags_BAGu_u_IN0)).
fof(12, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/bag/BAG__IN__BAG__FILTER', ah4s_numerals_numeralu_u_distribu_c17)).
# SZS output end CNFRefutation
