A certified basis of 6 identities
This list of identities is a basis, proved in Lean, of 77 semigroups of order six, all of which generate the variety V[7397]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-58c36e5830e8f53a in the data of the bases-min seal.
Certified for
[6, 7397] [6, 7399] [6, 7401] [6, 7415] [6, 7416] [6, 7484] [6, 7486] [6, 7492] [6, 7797] [6, 7799] [6, 7808] [6, 7835] [6, 7837] [6, 7843] [6, 7951] [6, 7955] [6, 7996] [6, 7998] [6, 8008] [6, 8011] [6, 8039] [6, 8041] [6, 8047] [6, 8126] [6, 8147] [6, 8151] [6, 8154] [6, 8245] [6, 8247] [6, 10556] [6, 10558] [6, 10560] [6, 10853] [6, 10855] [6, 10879] [6, 11026] [6, 11029] [6, 11037] [6, 11039] [6, 11069] [6, 11079] [6, 11080] [6, 11082] [6, 11281] [6, 11401] [6, 12563] [6, 12565] [6, 12571] [6, 12627] [6, 12634] [6, 12666] [6, 12688] [6, 12690] [6, 12707] [6, 12793] [6, 12906] [6, 12908] [6, 12910] [6, 12911] [6, 12915] [6, 12932] [6, 12934] [6, 12936] [6, 12938] [6, 12979] [6, 12981] [6, 12984] [6, 13344] [6, 13345] [6, 13347] [6, 13353] [6, 13354] [6, 13381] [6, 13923] [6, 13925] [6, 13931] [6, 14117]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyx ≈ xyxy
- xyzx ≈ xzyx
- xyzy ≈ xzyz