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[3057]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-6165771124af148c in the data of the bases-min seal.

Certified for

[6, 3057] [6, 6656] [6, 6675] [6, 6690] [6, 6699] [6, 6713] [6, 6721] [6, 6724] [6, 6728]

The identities

x² ≈ x³
xy ≈ xy²
x²y ≈ xyx
x²y ≈ yxy