# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:?[X6]:((p(s(t_bool,X6))<=>s(X1,X5)=s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X3))))&?[X7]:((p(s(t_bool,X7))<=>s(X1,X5)=s(X1,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(X1),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)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X1),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2)))))=s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_bools_cond(s(t_bool,X7),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)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X1),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_bools_cond(s(t_bool,X6),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),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)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X1),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4),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)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X1),X3))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))))))))),file('i/f/ringNorm/canonical__sum__simplify__def_c0', ch4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c0)).
fof(4, axiom,![X1]:![X2]:![X14]:![X4]: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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2)))))=s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))),file('i/f/ringNorm/canonical__sum__simplify__def_c0', ah4s_canonicals_canonicalu_u_sumu_u_simplifyu_u_defu_c1)).
fof(5, axiom,![X1]:![X2]:![X14]:![X4]:![X5]:?[X6]:((p(s(t_bool,X6))<=>s(X1,X5)=s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))))&?[X7]:((p(s(t_bool,X7))<=>s(X1,X5)=s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))))&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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2)))))=s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_bools_cond(s(t_bool,X7),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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_bools_cond(s(t_bool,X6),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X4),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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4),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)),h4s_canonicals_canonicalu_u_sumu_u_simplify(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X14))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))))))))),file('i/f/ringNorm/canonical__sum__simplify__def_c0', ah4s_canonicals_canonicalu_u_sumu_u_simplifyu_u_defu_c0)).
fof(7, axiom,![X1]:![X3]:s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(X1),X3)))=s(t_fun(t_h4s_canonicals_canonicalu_u_sum(X1),t_h4s_canonicals_canonicalu_u_sum(X1)),h4s_canonicals_canonicalu_u_sumu_u_simplify(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__simplify__def_c0', ah4s_ringNorms_ru_u_canonicalu_u_sumu_u_simplifyu_u_def)).
fof(8, 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__simplify__def_c0', ah4s_rings_semiu_u_ringu_u_ofu_u_def)).
fof(9, axiom,![X1]:![X15]:![X10]:![X16]:![X17]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,X17),s(X1,X16),s(t_fun(X1,t_fun(X1,X1)),X10),s(t_fun(X1,t_fun(X1,X1)),X15)))))=s(X1,X17),file('i/f/ringNorm/canonical__sum__simplify__def_c0', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c0)).
fof(10, axiom,![X1]:![X15]:![X10]:![X16]:![X17]:s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,X17),s(X1,X16),s(t_fun(X1,t_fun(X1,X1)),X10),s(t_fun(X1,t_fun(X1,X1)),X15)))))=s(X1,X16),file('i/f/ringNorm/canonical__sum__simplify__def_c0', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1)).
# SZS output end CNFRefutation
