# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(X1,happ(s(t_fun(t_h4s_lists_list(X1),X1),h4s_lists_hd),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_suc(s(t_h4s_nums_num,X2)))))))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/list/HD__GENLIST', ch4s_lists_HDu_u_GENLIST)).
fof(21, axiom,![X1]:![X5]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X2))))=>s(X1,happ(s(t_fun(t_h4s_lists_list(X1),X1),h4s_lists_el(s(t_h4s_nums_num,X5))),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(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,X5)))),file('i/f/list/HD__GENLIST', ah4s_lists_ELu_u_GENLIST)).
fof(22, axiom,![X1]:s(t_fun(t_h4s_lists_list(X1),X1),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0)))=s(t_fun(t_h4s_lists_list(X1),X1),h4s_lists_hd),file('i/f/list/HD__GENLIST', ah4s_lists_ELu_u_restrictedu_c0)).
fof(54, axiom,![X2]:![X30]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X30),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X30))),s(t_h4s_nums_num,X2))),file('i/f/list/HD__GENLIST', ah4s_arithmetics_LESSu_u_EQ)).
fof(55, axiom,![X2]:![X30]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X30),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X30))))),file('i/f/list/HD__GENLIST', ah4s_arithmetics_NOTu_u_LESS)).
fof(56, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/list/HD__GENLIST', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
# SZS output end CNFRefutation
