A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 81 semigroups of order six, all of which generate the variety V[3306]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-48a47dc95948f568 in the data of the bases-min seal.
Certified for
[6, 3306] [6, 3310] [6, 3314] [6, 3390] [6, 3448] [6, 3450] [6, 3513] [6, 6035] [6, 6038] [6, 6041] [6, 6119] [6, 6125] [6, 6126] [6, 6142] [6, 6184] [6, 6218] [6, 6328] [6, 6401] [6, 7315] [6, 7340] [6, 7363] [6, 7379] [6, 7385] [6, 7446] [6, 7451] [6, 7465] [6, 7472] [6, 7478] [6, 7480] [6, 7511] [6, 7517] [6, 7529] [6, 7530] [6, 7531] [6, 7627] [6, 7635] [6, 7652] [6, 7656] [6, 7657] [6, 7660] [6, 7713] [6, 8622] [6, 8724] [6, 8767] [6, 9868] [6, 10044] [6, 10108] [6, 10152] [6, 10260] [6, 10294] [6, 10323] [6, 10496] [6, 10504] [6, 10507] [6, 10512] [6, 10521] [6, 10526] [6, 10528] [6, 10529] [6, 10531] [6, 10541] [6, 10547] [6, 10574] [6, 10575] [6, 10576] [6, 10577] [6, 10581] [6, 10595] [6, 10602] [6, 10614] [6, 10617] [6, 10618] [6, 10621] [6, 10659] [6, 10720] [6, 10799] [6, 11130] [6, 11421] [6, 11439] [6, 11530] [6, 11654]
The identities
- x² ≈ x³
- x²y² ≈ xyx
- xy²z ≈ xyz