# 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_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_prod),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),X3),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),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_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),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_canonicalu_u_sumu_u_scalar3),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),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_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_prod),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),X2))))),file('i/f/ratRing/rat__ring__thms_c33', ch4s_ratRings_ratu_u_ringu_u_thmsu_c33)).
fof(4, axiom,![X10]:![X1]:![X2]:![X12]:![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_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(X10),X12))),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),X1))))),s(t_h4s_canonicals_canonicalu_u_sum(X10),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_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(X10),X12))),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_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(X10),X12))),s(X10,X4))),s(t_h4s_lists_list(t_h4s_quotes_index),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X10),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_canonicals_canonicalu_u_sum(X10),t_fun(t_h4s_canonicals_canonicalu_u_sum(X10),t_h4s_canonicals_canonicalu_u_sum(X10))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(X10),X12))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X10),X2))))),file('i/f/ratRing/rat__ring__thms_c33', ah4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c0)).
fof(7, 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_c33', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def)).
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_canonicalu_u_sumu_u_scalar3)=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_canonicalu_u_sumu_u_scalar3(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_c33', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def)).
fof(9, 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_prod)=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_prod(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_c33', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_produ_u_def)).
# SZS output end CNFRefutation
