# 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_monomu_u_insert(s(t_h4s_rings_ring(X1),X3))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))),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_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X5),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_monom(s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(X1),X3))),s(X1,X6))),s(X1,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(X1),X3))))),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),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)),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),X5))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))))),file('i/f/ringNorm/monom__insert__def_c1', ch4s_ringNorms_monomu_u_insertu_u_defu_c1)).
fof(6, 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/monom__insert__def_c1', ah4s_ringNorms_ru_u_monomu_u_insertu_u_def)).
fof(8, axiom,![X1]:![X2]:![X19]:![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_monomu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X19))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))),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_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),X5),s(t_h4s_lists_list(t_h4s_quotes_index),X4))),s(t_h4s_canonicals_canonicalu_u_sum(X1),h4s_canonicals_consu_u_monom(s(X1,X6),s(t_h4s_lists_list(t_h4s_quotes_index),X5),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_monom(s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X19))),s(X1,X6))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X19))))),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),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)),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),X19))),s(X1,X6))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))))),file('i/f/ringNorm/monom__insert__def_c1', ah4s_canonicals_monomu_u_insertu_u_defu_c1)).
fof(11, 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/monom__insert__def_c1', ah4s_rings_semiu_u_ringu_u_ofu_u_def)).
fof(18, axiom,![X1]:![X16]:![X12]:![X17]:![X18]:s(t_fun(X1,t_fun(X1,X1)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),h4s_semiu_u_rings_semiu_u_ring0(s(X1,X18),s(X1,X17),s(t_fun(X1,t_fun(X1,X1)),X12),s(t_fun(X1,t_fun(X1,X1)),X16)))))=s(t_fun(X1,t_fun(X1,X1)),X12),file('i/f/ringNorm/monom__insert__def_c1', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
fof(19, axiom,![X1]:![X16]:![X12]:![X17]:![X18]: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,X18),s(X1,X17),s(t_fun(X1,t_fun(X1,X1)),X12),s(t_fun(X1,t_fun(X1,X1)),X16)))))=s(X1,X17),file('i/f/ringNorm/monom__insert__def_c1', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1)).
# SZS output end CNFRefutation
