A certified basis of 15 identities
This list of identities is a basis, proved in Lean, of 11 semigroups of order six, all of which generate the variety V[3812]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-bbc2845542f5a0ae in the data of the bases-min seal.
Certified for
[6, 3812] [6, 3814] [6, 3825] [6, 3827] [6, 3938] [6, 3941] [6, 3947] [6, 6435] [6, 6436] [6, 6442] [6, 6443]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²yzy ≈ x²zy²
- x²yzy ≈ xyxzy
- x²yzy ≈ xy²zx
- x²yzy ≈ xyzxy
- x²yzy ≈ xyzyx
- x²yzy ≈ xzxy²
- x²yzy ≈ xzyxy
- x²yzy ≈ xzy²x
- xyxzx ≈ xzxyx
- xy²z² ≈ xzy²z