A certified basis of 10 identities

This list of identities is a basis, proved in Lean, of 5 semigroups of order six, all of which generate the variety V[9937]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-ee8e60fd4b43fb91 in the data of the bases-min seal.

Certified for

The identities

1. x² ≈ x⁴
2. x³y ≈ xyx²
3. x³yx ≈ xyx
4. x²y ≈ x²yx²
5. xyx ≈ xyx³
6. xyxy ≈ xy²x
7. xyx²zx ≈ xyzx
8. xyzxy ≈ xyzyx
9. xyzxz ≈ xyz²x
10. xyztxz ≈ xyztzx