A certified basis of 9 identities
This list of identities is a basis, proved in Lean, of 15 semigroups of order six, all of which generate the variety V[2849]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-3dc7e012ed637e7e in the data of the bases-min seal.
Certified for
[6, 2849] [6, 2865] [6, 2887] [6, 2901] [6, 5300] [6, 5308] [6, 5314] [6, 5322] [6, 5398] [6, 5484] [6, 5490] [6, 5875] [6, 5882] [6, 9352] [6, 9397]
The identities
- x³ ≈ x⁵
- x²y ≈ xyx
- x²y ≈ yx²
- x⁴y ≈ x²y
- x³y ≈ xy³
- x²y ≈ x²y³
- xyz ≈ xzy
- xyz ≈ yxz
- x³yz ≈ xyz