A certified basis of 32 identities
This list of identities is a basis, proved in Lean, of 4 semigroups of order six, all of which generate the variety V[10950]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ecccb8e02bc120d2 in the data of the bases-min seal.
Certified for
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx ≈ xyx²
- x²yx² ≈ xyx
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y³ ≈ xyx
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- x³y² ≈ x²yxy
- x³y² ≈ x²y²x
- x³y² ≈ xyx²y
- x³y² ≈ xyxyx
- x³y² ≈ xy²x²
- x²yxz ≈ xyx²z
- x²y²z ≈ xyxyz
- x²y²z ≈ xy²xz
- x²yzx ≈ xyxzx
- x²yzx ≈ xyzx²
- x²yzy ≈ xyxzy
- x²yzy ≈ xy²zx
- x²yzy ≈ xyzxy
- x²yzy ≈ xyzyx
- xyxz² ≈ xyzxz
- xyxz² ≈ xyz²x
- xy²zy ≈ xyzy²
- xy²z² ≈ xyzyz
- xy²z² ≈ xyz²y
- xyxztz ≈ xyzxtz
- xyxztz ≈ xyzxtz