# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_monomu_u_insert),s(t_h4s_integers_int,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_h4s_integers_int,X5))),s(t_h4s_integers_int,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_consu_u_monom(s(t_h4s_integers_int,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_monomu_u_insert),s(t_h4s_integers_int,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1))))))),file('i/f/integerRing/int__ring__thms_c18', ch4s_integerRings_intu_u_ringu_u_thmsu_c18)).
fof(9, axiom,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_monomu_u_insert)=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))),file('i/f/integerRing/int__ring__thms_c18', ah4s_integerRings_intu_u_ru_u_monomu_u_insertu_u_def)).
fof(13, axiom,![X6]:![X1]:![X22]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6))),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X6),X22))),s(X6,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_canonicals_consu_u_monom(s(X6,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X6),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_lists_list(t_h4s_quotes_index),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_canonicals_consu_u_monom(s(X6,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_canonicals_consu_u_monom(s(X6,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X6),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_canonicals_consu_u_monom(s(X6,happ(s(t_fun(X6,X6),happ(s(t_fun(X6,t_fun(X6,X6)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X6),X22))),s(X6,X5))),s(X6,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X6),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X6),h4s_canonicals_consu_u_monom(s(X6,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X6),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6))),happ(s(t_fun(X6,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X6),t_h4s_canonicals_canonicalu_u_sum(X6)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X6),X22))),s(X6,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X6),X1))))))),file('i/f/integerRing/int__ring__thms_c18', ah4s_ringNorms_monomu_u_insertu_u_defu_c0)).
fof(17, axiom,![X6]:![X23]:![X24]:![X11]:![X25]:![X26]:s(t_fun(X6,t_fun(X6,X6)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X6),h4s_rings_ring0(s(X6,X26),s(X6,X25),s(t_fun(X6,t_fun(X6,X6)),X11),s(t_fun(X6,t_fun(X6,X6)),X24),s(t_fun(X6,X6),X23)))))=s(t_fun(X6,t_fun(X6,X6)),X11),file('i/f/integerRing/int__ring__thms_c18', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
