# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X3))),s(t_h4s_lists_list(X1),h4s_lists_snoc(s(X1,X2),s(t_h4s_lists_list(X1),X3)))))=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),h4s_lists_nil))),file('i/f/rich_list/SEG__LENGTH__SNOC', ch4s_richu_u_lists_SEGu_u_LENGTHu_u_SNOC)).
fof(8, axiom,![X1]:![X3]:![X14]:s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(X1),h4s_lists_nil),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_richu_u_lists_SEG0u_c0)).
fof(9, axiom,![X1]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_lists_LENGTH0u_c0)).
fof(13, axiom,![X1]:![X2]:![X16]:![X3]:s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),X3)))))=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(X1),X3))))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_richu_u_lists_SEG0u_c1)).
fof(15, axiom,![X1]:![X10]:![X15]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X15))),s(t_h4s_lists_list(X1),X10)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X10))))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_lists_LENGTH0u_c1)).
fof(22, axiom,![X1]:![X2]:![X3]:s(t_h4s_lists_list(X1),h4s_lists_snoc(s(X1,X2),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),h4s_lists_nil))))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_lists_SNOCu_u_APPEND)).
fof(28, axiom,![X12]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X12))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(29, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_ONE)).
fof(45, axiom,![X12]:![X16]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X16))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_LESSu_u_EQu_u_MONO)).
fof(53, axiom,![X12]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12)))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(54, axiom,![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X16),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_ADDu_u_0)).
fof(64, axiom,![X1]:![X12]:![X16]:![X37]:![X38]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X38))),s(t_h4s_nums_num,X16))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X37)))))))=>s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X16),s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X38),s(t_h4s_lists_list(X1),X37)))))=s(t_h4s_lists_list(X1),h4s_richu_u_lists_seg(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X38))))),s(t_h4s_lists_list(X1),X37)))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_richu_u_lists_SEGu_u_APPEND2)).
fof(84, axiom,![X39]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X39),s(t_h4s_nums_num,X39)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(90, axiom,![X12]:![X16]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X12))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X12))))|s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,X12))),file('i/f/rich_list/SEG__LENGTH__SNOC', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
# SZS output end CNFRefutation
