A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 68 semigroups of order six, all of which generate the variety V[2846]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-86e214197d52f438 in the data of the bases-min seal.
Certified for
[6, 2846] [6, 2853] [6, 2864] [6, 2866] [6, 2868] [6, 2876] [6, 2877] [6, 2883] [6, 2884] [6, 2891] [6, 2900] [6, 2902] [6, 5299] [6, 5301] [6, 5307] [6, 5309] [6, 5310] [6, 5312] [6, 5313] [6, 5315] [6, 5321] [6, 5323] [6, 5377] [6, 5434] [6, 5482] [6, 5486] [6, 5489] [6, 5491] [6, 5492] [6, 5495] [6, 5497] [6, 5500] [6, 5501] [6, 5502] [6, 5503] [6, 5506] [6, 5508] [6, 5511] [6, 5512] [6, 5734] [6, 5735] [6, 5741] [6, 5743] [6, 5745] [6, 5748] [6, 5749] [6, 5755] [6, 5757] [6, 5759] [6, 5871] [6, 5874] [6, 5876] [6, 5878] [6, 5881] [6, 5883] [6, 9342] [6, 9368] [6, 9395] [6, 9399] [6, 9530] [6, 9532] [6, 9533] [6, 9607] [6, 9648] [6, 9654] [6, 9660] [6, 9661] [6, 9664]
The identities
- x³ ≈ x⁵
- xy ≈ yx
- x⁴y ≈ x²y
- x²y ≈ x²y³
- x³yz ≈ xyz