A certified basis of 8 identities

This list of identities is a basis, proved in Lean, of 5 semigroups of order six, all of which generate the variety V[12965]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-390769cc381d8736 in the data of the bases-min seal.

Certified for

The identities

1. x² ≈ x³
2. x²yx ≈ xyx
3. xyx ≈ xyx²
4. x²y² ≈ xyxy
5. xyxzx ≈ xyzx
6. x²y²z ≈ xy²xz
7. x²yzy ≈ xyxzy
8. xyxz² ≈ xyzxz