A certified basis of 11 identities
This list of identities is a basis, proved in Lean, of 20 semigroups of order six, all of which generate the variety V[6198]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-6c3c8e2fa94f7a52 in the data of the bases-min seal.
Certified for
[6, 6198] [6, 6484] [6, 6515] [6, 6601] [6, 6887] [6, 7030] [6, 9852] [6, 9928] [6, 10836] [6, 10841] [6, 10845] [6, 11310] [6, 11313] [6, 11316] [6, 11317] [6, 11322] [6, 11323] [6, 11417] [6, 11458] [6, 11688]
The identities
- x² ≈ x⁴
- xy ≈ xy³
- x³y ≈ xyx²
- x³yx ≈ xyx
- x²y ≈ x²yx²
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyxy ≈ xy²x
- xyz ≈ xyzy²
- xyzxy ≈ xyzyx
- xyzxz ≈ xyz²x