# 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_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge),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),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2))))),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),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_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),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),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_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2))),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),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,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,h4s_integers_intu_u_1))),s(t_h4s_integers_int,h4s_integers_intu_u_1))),s(t_h4s_lists_list(t_h4s_quotes_index),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_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X3),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_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge),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),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),X1))))))),file('i/f/integerRing/int__ring__thms_c14', ch4s_integerRings_intu_u_ringu_u_thmsu_c14)).
fof(6, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),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_canonicalu_u_sumu_u_merge(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_c14', ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def)).
fof(9, axiom,![X5]:![X1]:![X2]:![X14]:![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_canonicals_canonicalu_u_sum(X5),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X5),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(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_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),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),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_canonicals_canonicalu_u_sum(X5),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X5),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(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_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),X14))),s(X5,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X5),X14))))),s(X5,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X5),X14))))),s(t_h4s_lists_list(t_h4s_quotes_index),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_canonicals_canonicalu_u_sum(X5),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X5),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2))),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),X3),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_canonicals_canonicalu_u_sum(X5),t_fun(t_h4s_canonicals_canonicalu_u_sum(X5),t_h4s_canonicals_canonicalu_u_sum(X5))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X5),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X5),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X5),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X5),X1))))))),file('i/f/integerRing/int__ring__thms_c14', ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c3)).
fof(15, axiom,![X5]:![X21]:![X22]:![X10]:![X23]:![X24]:s(X5,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X5),h4s_rings_ring0(s(X5,X24),s(X5,X23),s(t_fun(X5,t_fun(X5,X5)),X10),s(t_fun(X5,t_fun(X5,X5)),X22),s(t_fun(X5,X5),X21)))))=s(X5,X23),file('i/f/integerRing/int__ring__thms_c14', ah4s_rings_ringu_u_accessorsu_c1)).
fof(16, axiom,![X5]:![X21]:![X22]:![X10]:![X23]:![X24]:s(t_fun(X5,t_fun(X5,X5)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X5),h4s_rings_ring0(s(X5,X24),s(X5,X23),s(t_fun(X5,t_fun(X5,X5)),X10),s(t_fun(X5,t_fun(X5,X5)),X22),s(t_fun(X5,X5),X21)))))=s(t_fun(X5,t_fun(X5,X5)),X10),file('i/f/integerRing/int__ring__thms_c14', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
