A certified basis of 19 identities

This list of identities is a basis, proved in Lean, of 9 semigroups of order six, all of which generate the variety V[1259]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-38c70246455c8806 in the data of the bases-min seal.

Certified for

The identities

1. x² ≈ x⁴
2. x³yx ≈ xyx
3. x²yx ≈ xyx²
4. x²yx² ≈ xyx
5. x²y² ≈ xyxy
6. x²y² ≈ xy²x
7. x²y² ≈ yx²y
8. xyx ≈ xyx³
9. x³y² ≈ yx³y
10. x²yzy ≈ x²zy²
11. x²yzy ≈ xyxzy
12. x²yzy ≈ xy²zx
13. x²yzy ≈ xyzxy
14. x²yzy ≈ xyzyx
15. x²yzy ≈ xzxy²
16. x²yzy ≈ xzyxy
17. x²yzy ≈ xzy²x
18. x²yzy ≈ yx²zy
19. xyxzx ≈ xzxyx