# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(~(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),X2)))))<=>?[X3]:p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X2))))))),file('i/f/list/NOT__NULL__MEM', ch4s_lists_NOTu_u_NULLu_u_MEM)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/list/NOT__NULL__MEM', aHLu_FALSITY)).
fof(11, axiom,![X1]:![X12]:(~(?[X5]:p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X5)))))<=>![X5]:~(p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X5)))))),file('i/f/list/NOT__NULL__MEM', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
fof(14, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/list/NOT__NULL__MEM', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(57, axiom,![X1]:![X2]:![X12]:(~(s(t_h4s_lists_list(X1),h4s_lists_filter(s(t_fun(X1,t_bool),X12),s(t_h4s_lists_list(X1),X2)))=s(t_h4s_lists_list(X1),X2))<=>?[X5]:(p(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X2))))))&~(p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X5))))))),file('i/f/list/NOT__NULL__MEM', ah4s_lists_FILTERu_u_NEQu_u_ID)).
fof(58, axiom,![X1]:![X2]:![X12]:(~(s(t_h4s_lists_list(X1),h4s_lists_filter(s(t_fun(X1,t_bool),X12),s(t_h4s_lists_list(X1),X2)))=s(t_h4s_lists_list(X1),h4s_lists_nil))<=>?[X5]:(p(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X2))))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X12),s(X1,X5)))))),file('i/f/list/NOT__NULL__MEM', ah4s_lists_FILTERu_u_NEQu_u_NIL)).
fof(63, axiom,![X1]:![X5]:![X28]:s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X28)))=s(t_bool,happ(s(t_fun(X1,t_bool),X28),s(X1,X5))),file('i/f/list/NOT__NULL__MEM', ah4s_bools_INu_u_DEF)).
fof(64, axiom,![X1]:![X5]:s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),h4s_lists_nil)))))=s(t_bool,f),file('i/f/list/NOT__NULL__MEM', ah4s_lists_MEMu_c0)).
fof(71, axiom,![X1]:![X2]:(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),X2))))<=>s(t_h4s_lists_list(X1),X2)=s(t_h4s_lists_list(X1),h4s_lists_nil)),file('i/f/list/NOT__NULL__MEM', ah4s_lists_NULLu_u_EQ)).
fof(80, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/list/NOT__NULL__MEM', aHLu_BOOLu_CASES)).
fof(81, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/list/NOT__NULL__MEM', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
