A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 15 semigroups of order six, all of which generate the variety V[7434]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-82211948a14ad896 in the data of the bases-min seal.
Certified for
[6, 7434] [6, 7435] [6, 7500] [6, 7823] [6, 7851] [6, 8027] [6, 8055] [6, 10919] [6, 12579] [6, 12642] [6, 12796] [6, 12982] [6, 13013] [6, 13050] [6, 13939]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyx ≈ xy²x
- xyx ≈ yxyx
- xyxz ≈ yxyz
- xyzx ≈ xzyx
- xy²zx ≈ xyzx