# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]: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,X4))),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_varlist(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,X4),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_varlist(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,X4))),s(t_h4s_integers_int,h4s_integers_intu_u_1))),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_varlist(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,X4))),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_c19', ch4s_integerRings_intu_u_ringu_u_thmsu_c19)).
fof(4, axiom,![X10]:![X12]:![X13]:![X7]:![X14]:![X15]:s(t_fun(X10,t_fun(X10,X10)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X10),h4s_rings_ring0(s(X10,X15),s(X10,X14),s(t_fun(X10,t_fun(X10,X10)),X7),s(t_fun(X10,t_fun(X10,X10)),X13),s(t_fun(X10,X10),X12)))))=s(t_fun(X10,t_fun(X10,X10)),X7),file('i/f/integerRing/int__ring__thms_c19', ah4s_rings_ringu_u_accessorsu_c2)).
fof(6, axiom,![X10]:![X1]:![X16]:![X2]:![X3]:![X4]:s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),happ(s(t_fun(X10,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X10),X16))),s(X10,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X10),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(X10),h4s_canonicals_consu_u_monom(s(X10,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_monom(s(X10,happ(s(t_fun(X10,X10),happ(s(t_fun(X10,t_fun(X10,X10)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X10),X16))),s(X10,X4))),s(X10,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X10),X16))))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X10),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X10),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),happ(s(t_fun(X10,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X10),X16))),s(X10,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))))))),file('i/f/integerRing/int__ring__thms_c19', ah4s_ringNorms_monomu_u_insertu_u_defu_c1)).
fof(8, 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_c19', ah4s_integerRings_intu_u_ru_u_monomu_u_insertu_u_def)).
fof(9, axiom,![X10]:![X12]:![X13]:![X7]:![X14]:![X15]:s(X10,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X10),h4s_rings_ring0(s(X10,X15),s(X10,X14),s(t_fun(X10,t_fun(X10,X10)),X7),s(t_fun(X10,t_fun(X10,X10)),X13),s(t_fun(X10,X10),X12)))))=s(X10,X14),file('i/f/integerRing/int__ring__thms_c19', ah4s_rings_ringu_u_accessorsu_c1)).
# SZS output end CNFRefutation
