A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 24 semigroups of order six, all of which generate the variety V[7167]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-5b34a6e1524ba3c4 in the data of the bases-min seal.
Certified for
[6, 7167] [6, 10164] [6, 10457] [6, 11986] [6, 12093] [6, 12147] [6, 12177] [6, 12197] [6, 12249] [6, 12285] [6, 12314] [6, 12331] [6, 12335] [6, 12338] [6, 12343] [6, 12344] [6, 12345] [6, 12350] [6, 12525] [6, 13855] [6, 14049] [6, 14202] [6, 14499] [6, 14522]
The identities
- x²y ≈ xy
- xy ≈ xy²
- xy ≈ xyxy
- xyxz ≈ xyz