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[13403]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-e50417ac27cea117 in the data of the bases-min seal.

Certified for

[6, 13403] [6, 13408] [6, 13409]

The identities

x² ≈ x³
xyx ≈ xy²x
xyx ≈ xyxyx
xyxzx ≈ xzxyx