# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_scalar2),s(t_h4s_lists_list(t_h4s_quotes_index),X1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),h4s_canonicals_nilu_u_monom),file('i/f/ratRing/rat__ring__thms_c29', ch4s_ratRings_ratu_u_ringu_u_thmsu_c29)).
fof(4, axiom,![X7]:![X9]:![X1]:s(t_h4s_canonicals_canonicalu_u_sum(X7),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X7),t_h4s_canonicals_canonicalu_u_sum(X7))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(X7),X9))),s(t_h4s_lists_list(t_h4s_quotes_index),X1))),s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom)))=s(t_h4s_canonicals_canonicalu_u_sum(X7),h4s_canonicals_nilu_u_monom),file('i/f/ratRing/rat__ring__thms_c29', ah4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c2)).
fof(5, axiom,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))),h4s_ratrings_ratu_u_ru_u_canonicalu_u_sumu_u_scalar2)=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))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(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_c29', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_scalar2u_u_def)).
# SZS output end CNFRefutation
