# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_canonicals_canonicalu_u_sum(X1),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(X1),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2)))=s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_nilu_u_monom),file('i/f/ringNorm/canonical__sum__prod__def_c2', ch4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c2)).
fof(4, axiom,![X1]:![X10]:![X2]:s(t_h4s_canonicals_canonicalu_u_sum(X1),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X10))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2)))=s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_nilu_u_monom),file('i/f/ringNorm/canonical__sum__prod__def_c2', ah4s_canonicals_canonicalu_u_sumu_u_produ_u_defu_c2)).
fof(5, axiom,![X1]:![X3]:s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(X1),X3)))=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),h4s_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(X1),X3))))),file('i/f/ringNorm/canonical__sum__prod__def_c2', ah4s_ringNorms_ru_u_canonicalu_u_sumu_u_produ_u_def)).
# SZS output end CNFRefutation
