A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 52 semigroups of order six, all of which generate the variety V[6211]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-896805617b072d1c in the data of the bases-min seal.
Certified for
[6, 6211] [6, 6494] [6, 6519] [6, 6525] [6, 6541] [6, 6607] [6, 6844] [6, 6903] [6, 6987] [6, 7046] [6, 8852] [6, 8883] [6, 8913] [6, 8923] [6, 9000] [6, 9025] [6, 9054] [6, 9064] [6, 9854] [6, 9930] [6, 9936] [6, 10817] [6, 10827] [6, 10835] [6, 10840] [6, 11147] [6, 11152] [6, 11363] [6, 11368] [6, 11371] [6, 11376] [6, 11377] [6, 11380] [6, 11382] [6, 11384] [6, 11393] [6, 11394] [6, 11454] [6, 11457] [6, 11512] [6, 11518] [6, 11524] [6, 11525] [6, 11526] [6, 11527] [6, 11528] [6, 11546] [6, 11597] [6, 11698] [6, 11739] [6, 11757] [6, 11780]
The identities
- x² ≈ x⁴
- x²y ≈ xyx