A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 45 semigroups of order six, all of which generate the variety V[3338]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-6b7ae10e0417a58f in the data of the bases-min seal.
Certified for
[6, 3338] [6, 3351] [6, 3358] [6, 3399] [6, 3569] [6, 3578] [6, 3581] [6, 3616] [6, 3617] [6, 3888] [6, 3894] [6, 3897] [6, 3917] [6, 6279] [6, 6571] [6, 7376] [6, 7381] [6, 7471] [6, 7475] [6, 7556] [6, 7572] [6, 7598] [6, 7608] [6, 7704] [6, 7705] [6, 7726] [6, 7729] [6, 7731] [6, 7784] [6, 7788] [6, 8301] [6, 8310] [6, 8522] [6, 8523] [6, 8529] [6, 8532] [6, 8534] [6, 8636] [6, 8688] [6, 10131] [6, 10153] [6, 10305] [6, 10325] [6, 11184] [6, 11565]
The identities
- x² ≈ x³
- xyx ≈ yx²
- xyz ≈ yxz