A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 3 semigroups of order six, all of which generate the variety V[2764]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-6c55eac57cbc8758 in the data of the bases-min seal.

Certified for

[6, 2764] [6, 5248] [6, 9307]

The identities

x³ ≈ x⁴
x²y ≈ xyx
x²y² ≈ yx²y
xyzy ≈ xzy²