A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 9 semigroups of order six, all of which generate the variety V[12178]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-d5a038c7a7eaf447 in the data of the bases-min seal.

Certified for

[6, 12178] [6, 12315] [6, 12351] [6, 14052] [6, 14203] [6, 14204] [6, 14594] [6, 14604] [6, 14607]

The identities

x²y ≈ xy
xy ≈ xy²
xy ≈ xyxy
xyxzx ≈ xyzx