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[6543]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-9c5ed0b88c00c88c in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³y ≈ xyx²
- x³yx ≈ xyx
- x²y ≈ x²yx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- xyx ≈ xyx³
- x³y² ≈ x²y²x
- x³y² ≈ xyx²y
- x²y³ ≈ xy²xy
- x²y³ ≈ xy³x
- x³yz ≈ xyx²z
- x³yz ≈ xyzx²
- x²y²z ≈ xy²xz
- x²yzy ≈ xyxzy
- xyxz² ≈ xyzxz
- xyxz² ≈ xyz²x
- xy³z ≈ xyzy²
- xy²z² ≈ xyz²y
- xyzxy ≈ xyzyx
- xyxztz ≈ xyzxtz
- xyxztz ≈ xyzxtz
- xyztxz ≈ xyztzx