A certified basis of 7 identities
This list of identities is a basis, proved in Lean, of 37 semigroups of order six, all of which generate the variety V[3464]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-a27067418a165b49 in the data of the bases-min seal.
Certified for
[6, 3464] [6, 3466] [6, 3492] [6, 3521] [6, 3535] [6, 3670] [6, 3671] [6, 3676] [6, 3689] [6, 3722] [6, 3734] [6, 3747] [6, 3750] [6, 3754] [6, 3782] [6, 3785] [6, 3832] [6, 6362] [6, 6363] [6, 6460] [6, 7884] [6, 7902] [6, 7920] [6, 7926] [6, 7961] [6, 8104] [6, 8107] [6, 8177] [6, 8248] [6, 8260] [6, 8539] [6, 8657] [6, 10728] [6, 10769] [6, 10777] [6, 10876] [6, 11571]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- xyzx ≈ xzyx