A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 45 semigroups of order six, all of which generate the variety V[7539]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-267448a22c8f8bb6 in the data of the bases-min seal.
Certified for
[6, 7539] [6, 7540] [6, 7543] [6, 7544] [6, 8287] [6, 8288] [6, 8289] [6, 8290] [6, 10415] [6, 10416] [6, 10419] [6, 10420] [6, 10635] [6, 10636] [6, 11157] [6, 11163] [6, 11164] [6, 13162] [6, 13163] [6, 13168] [6, 13169] [6, 13174] [6, 13175] [6, 13176] [6, 13177] [6, 13178] [6, 13179] [6, 13180] [6, 13181] [6, 13182] [6, 13183] [6, 13186] [6, 13187] [6, 13189] [6, 13190] [6, 13191] [6, 13580] [6, 13581] [6, 13582] [6, 13583] [6, 13584] [6, 13964] [6, 13965] [6, 14339] [6, 14340]
The identities
- x² ≈ x³
- xyx ≈ xy²