# 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(5, 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(6, axiom,![X5]:![X1]:![X13]:![X2]:![X3]:![X4]:s(t_h4s_canonicals_canonicalu_u_sum(X5),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),happ(s(t_fun(X5,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X5),X13))),s(X5,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X5),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X5),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(X5),h4s_canonicals_consu_u_monom(s(X5,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X5),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_monom(s(X5,happ(s(t_fun(X5,X5),happ(s(t_fun(X5,t_fun(X5,X5)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X5),X13))),s(X5,X4))),s(X5,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X5),X13))))),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X5),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X2),s(t_h4s_canonicals_canonicalu_u_sum(X5),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),happ(s(t_fun(X5,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X5),X13))),s(X5,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X1))))))),file('i/f/integerRing/int__ring__thms_c19', ah4s_ringNorms_monomu_u_insertu_u_defu_c1)).
fof(10, axiom,![X5]:![X14]:![X15]:![X10]:![X16]:![X17]:s(t_fun(X5,t_fun(X5,X5)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X5),h4s_rings_ring0(s(X5,X17),s(X5,X16),s(t_fun(X5,t_fun(X5,X5)),X10),s(t_fun(X5,t_fun(X5,X5)),X15),s(t_fun(X5,X5),X14)))))=s(t_fun(X5,t_fun(X5,X5)),X10),file('i/f/integerRing/int__ring__thms_c19', ah4s_rings_ringu_u_accessorsu_c2)).
fof(11, axiom,![X5]:![X14]:![X15]:![X10]:![X16]:![X17]:s(X5,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X5),h4s_rings_ring0(s(X5,X17),s(X5,X16),s(t_fun(X5,t_fun(X5,X5)),X10),s(t_fun(X5,t_fun(X5,X5)),X15),s(t_fun(X5,X5),X14)))))=s(X5,X16),file('i/f/integerRing/int__ring__thms_c19', ah4s_rings_ringu_u_accessorsu_c1)).
# SZS output end CNFRefutation
