# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),h4s_ratrings_ratu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_rats_rat),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_ringNorms_polynom(t_h4s_rats_rat)),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_ringNorms_polynom(t_h4s_rats_rat))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(t_h4s_rats_rat),X2))),s(t_h4s_ringNorms_polynom(t_h4s_rats_rat),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_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),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),h4s_ratrings_ratu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_rats_rat),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),h4s_ratrings_ratu_u_polynomu_u_normalize),s(t_h4s_ringNorms_polynom(t_h4s_rats_rat),X1))))),file('i/f/ratRing/rat__ring__thms_c54', ch4s_ratRings_ratu_u_ringu_u_thmsu_c54)).
fof(7, axiom,s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),h4s_ratrings_ratu_u_polynomu_u_normalize)=s(t_fun(t_h4s_ringNorms_polynom(t_h4s_rats_rat),t_h4s_canonicals_canonicalu_u_sum(t_h4s_rats_rat)),h4s_ringnorms_polynomu_u_normalize(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_c54', ah4s_ratRings_ratu_u_polynomu_u_normalizeu_u_def)).
fof(10, 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_c54', ah4s_ratRings_ratu_u_ru_u_canonicalu_u_sumu_u_produ_u_def)).
fof(18, axiom,![X3]:![X30]:![X1]:![X2]:s(t_h4s_canonicals_canonicalu_u_sum(X3),happ(s(t_fun(t_h4s_ringNorms_polynom(X3),t_h4s_canonicals_canonicalu_u_sum(X3)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X3),X30))),s(t_h4s_ringNorms_polynom(X3),happ(s(t_fun(t_h4s_ringNorms_polynom(X3),t_h4s_ringNorms_polynom(X3)),happ(s(t_fun(t_h4s_ringNorms_polynom(X3),t_fun(t_h4s_ringNorms_polynom(X3),t_h4s_ringNorms_polynom(X3))),h4s_ringnorms_pmult),s(t_h4s_ringNorms_polynom(X3),X2))),s(t_h4s_ringNorms_polynom(X3),X1)))))=s(t_h4s_canonicals_canonicalu_u_sum(X3),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X3),t_h4s_canonicals_canonicalu_u_sum(X3)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X3),t_fun(t_h4s_canonicals_canonicalu_u_sum(X3),t_h4s_canonicals_canonicalu_u_sum(X3))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(X3),X30))),s(t_h4s_canonicals_canonicalu_u_sum(X3),happ(s(t_fun(t_h4s_ringNorms_polynom(X3),t_h4s_canonicals_canonicalu_u_sum(X3)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X3),X30))),s(t_h4s_ringNorms_polynom(X3),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X3),happ(s(t_fun(t_h4s_ringNorms_polynom(X3),t_h4s_canonicals_canonicalu_u_sum(X3)),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(X3),X30))),s(t_h4s_ringNorms_polynom(X3),X1))))),file('i/f/ratRing/rat__ring__thms_c54', ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c3)).
# SZS output end CNFRefutation
