# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),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_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X2))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_rats_rat,t_h4s_rats_rat),happ(s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_add),s(t_h4s_rats_rat,X6))),s(t_h4s_rats_rat,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X2))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))))),file('i/f/ratRing/rat__ring__thms_c11', ch4s_ratRings_ratu_u_ringu_u_thmsu_c11)).
fof(4, axiom,![X12]:![X1]:![X2]:![X14]:![X3]:![X4]:![X5]:![X6]:s(t_h4s_canonicals_canonicalu_u_sum(X12),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X12),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X12),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X12),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X12),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(X12),h4s_canonicals_consu_u_monom(s(X12,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X12),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X12),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X12),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X12),X1))))))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,happ(s(t_fun(X12,X12),happ(s(t_fun(X12,t_fun(X12,X12)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X12),X14))),s(X12,X6))),s(X12,X5))),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X12),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X12),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X12),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X12),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X3),s(t_h4s_canonicals_canonicalu_u_sum(X12),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_fun(t_h4s_canonicals_canonicalu_u_sum(X12),t_h4s_canonicals_canonicalu_u_sum(X12))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X12),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X12),h4s_canonicals_consu_u_monom(s(X12,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X12),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X12),X1))))))),file('i/f/ratRing/rat__ring__thms_c11', ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c0)).
fof(11, axiom,s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_merge)=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(t_h4s_rats_rat),h4s_rings_ring0(s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(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_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_add),s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_rats_rat,t_h4s_rats_rat)),h4s_rats_ratu_u_mul),s(t_fun(t_h4s_rats_rat,t_h4s_rats_rat),h4s_rats_ratu_u_ainv))))),file('i/f/ratRing/rat__ring__thms_c11', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def)).
fof(13, axiom,![X12]:![X21]:![X22]:![X9]:![X23]:![X24]:s(t_fun(X12,t_fun(X12,X12)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X12),h4s_rings_ring0(s(X12,X24),s(X12,X23),s(t_fun(X12,t_fun(X12,X12)),X9),s(t_fun(X12,t_fun(X12,X12)),X22),s(t_fun(X12,X12),X21)))))=s(t_fun(X12,t_fun(X12,X12)),X9),file('i/f/ratRing/rat__ring__thms_c11', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
