A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 76 semigroups of order six, all of which generate the variety V[4016]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-e3ee83e538593760 in the data of the bases-min seal.
Certified for
[6, 4016] [6, 4115] [6, 4124] [6, 4222] [6, 4231] [6, 4321] [6, 5926] [6, 6047] [6, 6739] [6, 6770] [6, 6834] [6, 6838] [6, 6847] [6, 6869] [6, 6916] [6, 6977] [6, 6981] [6, 6990] [6, 7012] [6, 8802] [6, 8814] [6, 8817] [6, 8820] [6, 8888] [6, 8901] [6, 8926] [6, 8928] [6, 8930] [6, 8931] [6, 8935] [6, 8938] [6, 8952] [6, 8964] [6, 8967] [6, 8970] [6, 9030] [6, 9042] [6, 9067] [6, 9069] [6, 9071] [6, 9072] [6, 9076] [6, 9079] [6, 9841] [6, 9847] [6, 9953] [6, 9959] [6, 10174] [6, 10176] [6, 10184] [6, 10185] [6, 10192] [6, 10200] [6, 10208] [6, 10220] [6, 10677] [6, 10678] [6, 10682] [6, 10683] [6, 10684] [6, 11619] [6, 11660] [6, 11713] [6, 11760] [6, 11762] [6, 11770] [6, 11771] [6, 11789] [6, 11794] [6, 11797] [6, 11802] [6, 11806] [6, 11808] [6, 11831] [6, 11843] [6, 11848]
The identities
- x³y ≈ xy
- xy ≈ xy³
- xy ≈ xyxyxy
- xyz ≈ xzy