A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 30 semigroups of order six, all of which generate the variety V[5535]. Removing the identities that follow from the others leaves 1 identity (Vampire); the variety page shows the shortest known basis.
Identifier sb-f7a22a88994559bc in the data of the bases-min seal.
Certified for
[6, 5535] [6, 5544] [6, 5565] [6, 5566] [6, 5567] [6, 5568] [6, 5584] [6, 5592] [6, 5598] [6, 5599] [6, 5600] [6, 5601] [6, 9415] [6, 9423] [6, 9424] [6, 9425] [6, 9426] [6, 9434] [6, 9435] [6, 9536] [6, 9549] [6, 9552] [6, 9553] [6, 9562] [6, 9567] [6, 9569] [6, 9570] [6, 9571] [6, 9701] [6, 9703]
The identities
- x³ ≈ x²y
- xyx ≈ xy²
- xyx ≈ xyz