A certified basis of 14 identities

This list of identities is a basis, proved in Lean, of 6 semigroups of order six, all of which generate the variety V[12950]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-faaf87b0e9e152d0 in the data of the bases-min seal.

Certified for

The identities

1. x² ≈ x³
2. x²yx ≈ xyx
3. xyx ≈ xyx²
4. xyx ≈ xy²x
5. x²y² ≈ xyxy
6. xyx ≈ xyxyx
7. x²y²z ≈ xyxz
8. xyxzx ≈ xyzx
9. xy²zx ≈ xyzx
10. xyzx ≈ xyzyx
11. xyzx ≈ xyz²x
12. x²yzy ≈ xyxzy
13. x²yzy ≈ xyzxy
14. xyxz² ≈ xyzxz