A certified basis of 25 identities
This list of identities is a basis, proved in Lean, of 7 semigroups of order six, all of which generate the variety V[8856]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-c790525aa7de6832 in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx² ≈ xyx
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y³ ≈ xyx
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- x³y² ≈ x²yxy
- x³y² ≈ x²y²x
- xyzx ≈ xzyx
- x²y²z ≈ xyxyz
- x²y²z ≈ xy²xz
- x²yzy ≈ xyxzy
- x²yzy ≈ xy²zx
- x²yzy ≈ xzxy²
- xy²zy ≈ xzyz²
- xy²z² ≈ xyzyz
- xy²z² ≈ xyz²y
- xy²z² ≈ xzy²z
- xyztx ≈ xytzx
- xyxztz ≈ xyzxtz
- xyxztz ≈ xyzxtz