A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 109 semigroups of order six, all of which generate the variety V[3164]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-09d3477792539051 in the data of the bases-min seal.
Certified for
[6, 3164] [6, 3165] [6, 3169] [6, 3170] [6, 4325] [6, 4326] [6, 4328] [6, 4329] [6, 4331] [6, 9963] [6, 9964] [6, 9965] [6, 9967] [6, 9969] [6, 9972] [6, 9974] [6, 11853] [6, 11854] [6, 11856] [6, 11857] [6, 11858] [6, 11859] [6, 11860] [6, 11862] [6, 11863] [6, 11865] [6, 11866] [6, 11869] [6, 11870] [6, 11871] [6, 11872] [6, 11874] [6, 11876] [6, 11879] [6, 11880] [6, 11882] [6, 11883] [6, 11884] [6, 11885] [6, 11898] [6, 11899] [6, 11902] [6, 11904] [6, 11909] [6, 11918] [6, 11919] [6, 11920] [6, 11922] [6, 11926] [6, 14608] [6, 14609] [6, 14611] [6, 14612] [6, 14614] [6, 14618] [6, 14619] [6, 14622] [6, 14623] [6, 14627] [6, 14629] [6, 14631] [6, 14636] [6, 14643] [6, 14645] [6, 14655] [6, 14656] [6, 14658] [6, 14659] [6, 14661] [6, 14665] [6, 14667] [6, 14669] [6, 14671] [6, 14675] [6, 14681] [6, 14684] [6, 14692] [6, 14694] [6, 14699] [6, 14703] [6, 14707] [6, 14709] [6, 14714] [6, 14718] [6, 14721] [6, 14725] [6, 14730] [6, 14732] [6, 14738] [6, 14740] [6, 14745] [6, 14752] [6, 14754] [6, 14772] [6, 14776] [6, 14787] [6, 14789] [6, 14802] [6, 14806] [6, 14820] [6, 14822] [6, 14838] [6, 14842] [6, 14846] [6, 14859] [6, 14861] [6, 14867] [6, 14874] [6, 14876]
The identities
- x ≈ x³
- xy ≈ yx