A certified basis of 15 identities
This list of identities is a basis, proved in Lean, of 15 semigroups of order six, all of which generate the variety V[1247]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-9980eddcfc47bb7a in the data of the bases-min seal.
Certified for
[6, 1247] [6, 1248] [6, 1256] [6, 1289] [6, 1290] [6, 1297] [6, 1333] [6, 1334] [6, 1342] [6, 1387] [6, 1388] [6, 1395] [6, 3001] [6, 3003] [6, 3037]
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- xyx ≈ xyx³
- x³y² ≈ yx³y
- x²yz ≈ xyxz
- xyzx ≈ xzyx
- xyzy ≈ xzy²
- x²yzy ≈ xy²zx
- x²yzy ≈ yx²zy
- xyzt ≈ xzyt