A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 39 semigroups of order six, all of which generate the variety V[5611]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-53c533611eec5f38 in the data of the bases-min seal.
Certified for
[6, 5611] [6, 5619] [6, 5629] [6, 5631] [6, 5633] [6, 5652] [6, 5656] [6, 5665] [6, 5673] [6, 5678] [6, 9438] [6, 9448] [6, 9454] [6, 9456] [6, 9459] [6, 9463] [6, 9470] [6, 9472] [6, 9580] [6, 9583] [6, 9584] [6, 9591] [6, 9600] [6, 9706] [6, 9709] [6, 9712] [6, 9715] [6, 9719] [6, 9722] [6, 9729] [6, 9732] [6, 9733] [6, 9734] [6, 9741] [6, 9743] [6, 9745] [6, 9756] [6, 9759] [6, 9769]
The identities
- x³ ≈ x⁴
- x²y ≈ xyx
- xyz ≈ xzy