# 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_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_lists_list(t_h4s_quotes_index),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_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),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_monomu_u_insert),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),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X4),s(t_h4s_lists_list(t_h4s_quotes_index),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_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_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),h4s_canonicals_consu_u_monom(s(t_h4s_rats_rat,X4),s(t_h4s_lists_list(t_h4s_quotes_index),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,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,X5))),s(t_h4s_rats_rat,X4))),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,X4),s(t_h4s_lists_list(t_h4s_quotes_index),X2),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_lists_list(t_h4s_quotes_index),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_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),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_monomu_u_insert),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))))))),file('i/f/ratRing/rat__ring__thms_c18', ch4s_ratRings_ratu_u_ringu_u_thmsu_c18)).
fof(8, axiom,s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),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_monomu_u_insert)=s(t_fun(t_h4s_rats_rat,t_fun(t_h4s_lists_list(t_h4s_quotes_index),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_monomu_u_insert(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_c18', ah4s_ratRings_ratu_u_ru_u_monomu_u_insertu_u_def)).
fof(13, axiom,![X6]:![X1]:![X20]:![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),X20))),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),X20))),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),X20))),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/ratRing/rat__ring__thms_c18', ah4s_ringNorms_monomu_u_insertu_u_defu_c0)).
fof(17, axiom,![X6]:![X21]:![X22]:![X11]:![X23]:![X24]:s(t_fun(X6,t_fun(X6,X6)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X6),h4s_rings_ring0(s(X6,X24),s(X6,X23),s(t_fun(X6,t_fun(X6,X6)),X11),s(t_fun(X6,t_fun(X6,X6)),X22),s(t_fun(X6,X6),X21)))))=s(t_fun(X6,t_fun(X6,X6)),X11),file('i/f/ratRing/rat__ring__thms_c18', ah4s_rings_ringu_u_accessorsu_c2)).
# SZS output end CNFRefutation
