A certified basis of 23 identities
This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[6882]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-72f0a3a19bcecb9f in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- xy ≈ xy³
- x³y ≈ yxy²
- x³yx ≈ xyx
- x³y² ≈ yxy
- x²y ≈ xyxy²
- x²y ≈ xy²xy
- x²y ≈ yx²y²
- x²y ≈ yxyxy
- x²y ≈ y²x²y
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²yxy ≈ yxy
- x²y² ≈ xyxy
- x²y² ≈ yx²y
- xyx ≈ yxy²x
- x²yz ≈ xyxz
- xy²zy ≈ xzy
- xyz ≈ xzyz²
- xyzx ≈ xzyx
- xyzy ≈ xzy²
- xyx²z ≈ zyxz²
- xyxz² ≈ zyx²z