A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 56 semigroups of order six, all of which generate the variety V[7157]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ba998b0f0373d94e in the data of the bases-min seal.
Certified for
[6, 7157] [6, 7160] [6, 7163] [6, 7201] [6, 7206] [6, 7207] [6, 7247] [6, 7251] [6, 7275] [6, 8753] [6, 8756] [6, 8759] [6, 10139] [6, 10143] [6, 10308] [6, 10313] [6, 10345] [6, 10355] [6, 11746] [6, 11982] [6, 12004] [6, 12049] [6, 12072] [6, 12168] [6, 12172] [6, 12247] [6, 12271] [6, 12276] [6, 12277] [6, 12282] [6, 12283] [6, 12291] [6, 12292] [6, 12298] [6, 12321] [6, 12323] [6, 12425] [6, 12433] [6, 12437] [6, 12438] [6, 12444] [6, 12459] [6, 12461] [6, 13851] [6, 13873] [6, 14186] [6, 14199] [6, 14212] [6, 14218] [6, 14321] [6, 14396] [6, 14403] [6, 14447] [6, 14450] [6, 14451] [6, 14452]
The identities
- x²y ≈ xy
- xyx ≈ yx²