# 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))),h4s_ringnorms_ru_u_varlistu_u_insert(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),h4s_canonicals_consu_u_monom(s(X1,X6),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_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),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),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,h4s_rings_ringu_u_r1(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))),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),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))),h4s_ringnorms_ru_u_varlistu_u_insert(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))))))),file('i/f/ringNorm/varlist__insert__def_c0', ch4s_ringNorms_varlistu_u_insertu_u_defu_c0)).
fof(4, axiom,![X1]:![X13]:![X9]:![X14]:![X15]: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,X15),s(X1,X14),s(t_fun(X1,t_fun(X1,X1)),X9),s(t_fun(X1,t_fun(X1,X1)),X13)))))=s(X1,X14),file('i/f/ringNorm/varlist__insert__def_c0', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1)).
fof(5, axiom,![X1]:![X13]:![X9]:![X14]:![X15]: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,X15),s(X1,X14),s(t_fun(X1,t_fun(X1,X1)),X9),s(t_fun(X1,t_fun(X1,X1)),X13)))))=s(t_fun(X1,t_fun(X1,X1)),X9),file('i/f/ringNorm/varlist__insert__def_c0', ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2)).
fof(6, axiom,![X1]:![X2]:![X16]:![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))),h4s_canonicals_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X16))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))),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),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_varlist(s(t_h4s_lists_list(t_h4s_quotes_index),X5),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),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),X16))),s(X1,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X16))))),s(X1,X6))),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_monom(s(X1,X6),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))),h4s_canonicals_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(X1),X16))),s(t_h4s_lists_list(t_h4s_quotes_index),X5))),s(t_h4s_canonicals_canonicalu_u_sum(X1),X2))))))),file('i/f/ringNorm/varlist__insert__def_c0', ah4s_canonicals_varlistu_u_insertu_u_defu_c0)).
fof(9, axiom,![X1]:![X3]: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))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(X1),X3)))=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))),h4s_canonicals_varlistu_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/varlist__insert__def_c0', ah4s_ringNorms_ru_u_varlistu_u_insertu_u_def)).
fof(10, 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/varlist__insert__def_c0', ah4s_rings_semiu_u_ringu_u_ofu_u_def)).
# SZS output end CNFRefutation
