A certified basis of 3 identities

This list of identities is a basis, proved in Lean, of 9 semigroups of order six, all of which generate the variety V[8827]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-676ada84b2b37817 in the data of the bases-min seal.

Certified for

[6, 8827] [6, 8836] [6, 8919] [6, 8977] [6, 8986] [6, 9060] [6, 10397] [6, 10404] [6, 11749]

The identities

x² ≈ x⁴
x³y ≈ xy
xyx ≈ yx²