# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]: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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(X1),X3))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_canonicals_canonicalu_u_sum(X1),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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X1),X3))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_lists_list(t_h4s_quotes_index),X5))))),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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(X1),X3))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))),file('i/f/ringNorm/canonical__sum__scalar3__def_c1', ch4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c1)).
fof(5, axiom,![X1]:![X2]:![X13]:![X4]:![X5]:![X6]: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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_canonicals_canonicalu_u_sumu_u_scalar3(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_canonicals_canonicalu_u_sum(X1),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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_canonicals_monomu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_lists_list(t_h4s_quotes_index),X5))))),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_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1))),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_canonicals_canonicalu_u_sumu_u_scalar3(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X13))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))),file('i/f/ringNorm/canonical__sum__scalar3__def_c1', ah4s_canonicals_canonicalu_u_sumu_u_scalar3u_u_defu_c1)).
fof(7, axiom,![X1]:![X3]:s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(X1),X3)))=s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_canonicals_canonicalu_u_sumu_u_scalar3(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__scalar3__def_c1', ah4s_ringNorms_ru_u_canonicalu_u_sumu_u_scalar3u_u_def)).
fof(8, axiom,![X1]:![X3]:s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(X1),X3)))=s(t_fun(X1,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)))),h4s_canonicals_monomu_u_insert(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__scalar3__def_c1', ah4s_ringNorms_ru_u_monomu_u_insertu_u_def)).
fof(9, axiom,![X1]:![X3]:s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(X1),X3)))=s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),X3))),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X3))),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X3))),s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(X1),X3))))),file('i/f/ringNorm/canonical__sum__scalar3__def_c1', ah4s_rings_semiu_u_ringu_u_ofu_u_def)).
# SZS output end CNFRefutation
