A certified basis of 15 identities
This list of identities is a basis, proved in Lean, of 10 semigroups of order six, all of which generate the variety V[11894]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-dd48a1ef9be1d98e in the data of the bases-min seal.
Certified for
[6, 11894] [6, 11914] [6, 14626] [6, 14641] [6, 14654] [6, 14679] [6, 14750] [6, 14769] [6, 14813] [6, 14832]
The identities
- x ≈ x³
- x²y ≈ xyxy²
- x²y ≈ xy²xy
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²yxy ≈ xy²
- x²y² ≈ xyxy
- xyx²y ≈ xy²
- x²yxz ≈ xyz
- x²yz ≈ xyxz
- xyx²z ≈ xyz
- xy²zy ≈ xzy
- xyz ≈ xzyz²
- xyzx ≈ xzyx
- xyzy ≈ xzy²