A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 49 semigroups of order six, all of which generate the variety V[2855]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-840c0e76ccb57ab6 in the data of the bases-min seal.
Certified for
[6, 2855] [6, 2857] [6, 2859] [6, 2861] [6, 2871] [6, 2873] [6, 2875] [6, 2880] [6, 2882] [6, 2893] [6, 2895] [6, 2897] [6, 5302] [6, 5304] [6, 5306] [6, 5311] [6, 5316] [6, 5318] [6, 5320] [6, 5451] [6, 5455] [6, 5459] [6, 5463] [6, 5493] [6, 5494] [6, 5504] [6, 5505] [6, 5737] [6, 5738] [6, 5739] [6, 5742] [6, 5751] [6, 5752] [6, 5753] [6, 5756] [6, 5877] [6, 5884] [6, 9377] [6, 9381] [6, 9385] [6, 9387] [6, 9578] [6, 9579] [6, 9594] [6, 9596] [6, 9603] [6, 9604] [6, 9612] [6, 9651]
The identities
- x³ ≈ x⁵
- xy ≈ yx