A certified basis of 5 identities

This list of identities is a basis, proved in Lean, of 7 semigroups of order six, all of which generate the variety V[5552]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-f63e0b6abbf55371 in the data of the bases-min seal.

Certified for

[6, 5552] [6, 5562] [6, 5570] [6, 5572] [6, 9548] [6, 9647] [6, 9653]

The identities

x³ ≈ x⁴
x²y ≈ xyx
x³y ≈ x²y
xy² ≈ xy³
xyz ≈ xzy