# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag),file('i/f/bag/BAG__FILTER__EMPTY', ch4s_bags_BAGu_u_FILTERu_u_EMPTY)).
fof(3, 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/BAG__FILTER__EMPTY', aHLu_EXT)).
fof(8, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,X11),s(X1,X10),s(X1,X10)))=s(X1,X10),file('i/f/bag/BAG__FILTER__EMPTY', ah4s_bools_CONDu_u_ID)).
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__FILTER__EMPTY', ah4s_bags_EMPTYu_u_BAG0)).
fof(12, axiom,![X9]:![X1]:![X8]:![X7]:s(X1,happ(s(t_fun(X9,X1),h4s_combins_k(s(X1,X7))),s(X9,X8)))=s(X1,X7),file('i/f/bag/BAG__FILTER__EMPTY', ah4s_combins_Ku_u_THM)).
fof(13, axiom,![X1]:![X11]:![X2]:![X7]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_filter(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_h4s_nums_num),X11))),s(X1,X7)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X7))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X11),s(X1,X7))),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/bag/BAG__FILTER__EMPTY', ah4s_bags_BAGu_u_FILTERu_u_DEF)).
# SZS output end CNFRefutation
