A certified basis of 29 identities
This list of identities is a basis, proved in Lean, of 4 semigroups of order six, all of which generate the variety V[413]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-240672651a58717d in the data of the bases-min seal.
Certified for
The identities
- x³ ≈ x²y
- x³ ≈ xyx
- x³ ≈ yxy
- x³ ≈ y²x
- x³ ≈ y³
- x²y ≈ xyx
- x²y ≈ yxy
- x²y ≈ y²x
- xyx ≈ yxy
- x³ ≈ y²z
- x³ ≈ yzy
- x²y ≈ x²z
- x²y ≈ xzx
- x²y ≈ y²z
- x²y ≈ yzy
- x²y ≈ zxz
- x²y ≈ zyz
- x²y ≈ z²y
- xyx ≈ xzx
- xyx ≈ yzy
- xyx ≈ zyz
- xyz ≈ xzy
- x²y ≈ z²t
- x²y ≈ ztz
- xyx ≈ ztz
- x³ ≈ yztu
- x²y ≈ ztuv
- xyx ≈ ztuv
- xyzt ≈ uvws