A certified basis of 30 identities
This list of identities is a basis, proved in Lean, of 2 semigroups of order six, all of which generate the variety V[4091]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-77af0a58570c83cc in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx² ≈ xyx
- x²y² ≈ xy²x
- xyx ≈ xyx³
- xyxy ≈ xy²x
- x²y³ ≈ xy³x
- x²yxz ≈ xyx²z
- x²yzx ≈ xyzx²
- x²yzy ≈ x²zy²
- x²yzy ≈ xyxzy
- x²yzy ≈ xyzyx
- x²yzy ≈ xzyxy
- x²yzy ≈ xzy²x
- xyxzx ≈ xzxyx
- xyxz² ≈ xzyxz
- xyxz² ≈ xz²yx
- xy²zy ≈ xyzy²
- x²yztz ≈ x²tzyz
- x²yztz ≈ xyzxtz
- x²yztz ≈ xyztzx
- x²yztz ≈ xtzxyz
- xyxztz ≈ xyxtz²
- xyxztz ≈ xzyxtz
- xyxztz ≈ xztzyx
- xyxztz ≈ xtzyxz
- xyxztz ≈ xtz²yx
- xyxztz ≈ xtz²yx
- xyxzt² ≈ xzt²yx
- xyxzt² ≈ xzt²yx