A certified basis of 7 identities
This list of identities is a basis, proved in Lean, of 13 semigroups of order six, all of which generate the variety V[12776]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-6a468971e954b7b4 in the data of the bases-min seal.
Certified for
[6, 12776] [6, 12886] [6, 12967] [6, 13058] [6, 13137] [6, 13668] [6, 13689] [6, 13716] [6, 13726] [6, 13736] [6, 14152] [6, 14262] [6, 14263]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- xyxzx ≈ xyzx
- x²yzy ≈ xyxzy
- xyxz² ≈ xyzxz