# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,X2))))))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/list/NULL__GENLIST', ch4s_lists_NULLu_u_GENLIST)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/list/NULL__GENLIST', aHLu_TRUTH)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f0)),file('i/f/list/NULL__GENLIST', aHLu_BOOLu_CASES)).
fof(12, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/list/NULL__GENLIST', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(13, axiom,![X4]:(s(t_bool,f0)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/list/NULL__GENLIST', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(15, axiom,![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,X2)))),file('i/f/list/NULL__GENLIST', ah4s_arithmetics_numu_u_CASES)).
fof(16, axiom,![X1]:![X3]:s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_lists_list(X1),h4s_lists_nil),file('i/f/list/NULL__GENLIST', ah4s_lists_GENLIST0u_c0)).
fof(17, axiom,![X1]:![X2]:![X3]:s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,X2)))))=s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),h4s_combins_o(s(t_fun(t_h4s_nums_num,X1),X3),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc))),s(t_h4s_nums_num,X2))))),file('i/f/list/NULL__GENLIST', ah4s_lists_GENLISTu_u_CONS)).
fof(18, axiom,![X1]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_bool,t),file('i/f/list/NULL__GENLIST', ah4s_lists_NULLu_u_DEFu_c0)).
fof(19, axiom,![X1]:![X4]:![X12]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X12),s(t_h4s_lists_list(X1),X4)))))=s(t_bool,f0),file('i/f/list/NULL__GENLIST', ah4s_lists_NULLu_u_DEFu_c1)).
# SZS output end CNFRefutation
