A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[6536]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-774ce6857d22f430 in the data of the bases-min seal.

Certified for

[6, 6536] [6, 6602]

The identities

x² ≈ x⁴
x³yx ≈ xyx
x²y² ≈ xyxy
xy²z ≈ xzy²