# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/list/NULL__FILTER', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/list/NULL__FILTER', 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/list/NULL__FILTER', aHLu_BOOLu_CASES)).
fof(9, axiom,![X7]:![X8]:![X9]:(~(s(t_h4s_lists_list(X7),h4s_lists_filter(s(t_fun(X7,t_bool),X9),s(t_h4s_lists_list(X7),X8)))=s(t_h4s_lists_list(X7),h4s_lists_nil))<=>?[X6]:(p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X7),X8))))))&p(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X6)))))),file('i/f/list/NULL__FILTER', ah4s_lists_FILTERu_u_NEQu_u_NIL)).
fof(11, axiom,![X7]:![X6]:![X9]:![X13]:(p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X7),h4s_lists_filter(s(t_fun(X7,t_bool),X9),s(t_h4s_lists_list(X7),X13))))))))<=>(p(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X6))))&p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X7),X13)))))))),file('i/f/list/NULL__FILTER', ah4s_lists_MEMu_u_FILTER)).
fof(13, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X7),X8)))))<=>?[X10]:p(s(t_bool,h4s_bools_in(s(X7,X10),s(t_fun(X7,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X7),X8))))))),file('i/f/list/NULL__FILTER', ah4s_lists_NOTu_u_NULLu_u_MEM)).
fof(27, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/list/NULL__FILTER', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(39, axiom,![X7]:s(t_h4s_lists_list(X7),h4s_lists_nil)=s(t_h4s_lists_list(X7),h4s_lists_u_20u_40indu_u_typelist0),file('i/f/list/NULL__FILTER', ah4s_lists_NIL0)).
fof(61, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/list/NULL__FILTER', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(94, axiom,![X7]:![X6]:![X25]:s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),X25)))=s(t_bool,happ(s(t_fun(X7,t_bool),X25),s(X7,X6))),file('i/f/list/NULL__FILTER', ah4s_bools_INu_u_DEF)).
fof(111, axiom,![X7]:p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X7),h4s_lists_nil)))),file('i/f/list/NULL__FILTER', ah4s_lists_NULL0u_c0)).
fof(133, conjecture,![X7]:![X50]:![X9]:(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X7),h4s_lists_filter(s(t_fun(X7,t_bool),X9),s(t_h4s_lists_list(X7),X50))))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X7,X6),s(t_fun(X7,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X7),X50))))))=>~(p(s(t_bool,happ(s(t_fun(X7,t_bool),X9),s(X7,X6))))))),file('i/f/list/NULL__FILTER', ch4s_lists_NULLu_u_FILTER)).
# SZS output end CNFRefutation
