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[4077]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-b7e86433e409f4de in the data of the bases-min seal.

Certified for

[6, 4077] [6, 4188] [6, 6370]

The identities

x² ≈ x⁴
x³yx ≈ xyx
xy²x ≈ yx²y
xyzx ≈ xzyx