A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 94 semigroups of order six, all of which generate the variety V[4327]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-eaae4750a00bfd4e in the data of the bases-min seal.
Certified for
[6, 4327] [6, 4330] [6, 9966] [6, 9968] [6, 9973] [6, 9975] [6, 11855] [6, 11861] [6, 11864] [6, 11873] [6, 11881] [6, 11886] [6, 11887] [6, 11889] [6, 11890] [6, 11891] [6, 11893] [6, 11900] [6, 11903] [6, 11906] [6, 11907] [6, 11908] [6, 11912] [6, 11921] [6, 11925] [6, 14610] [6, 14613] [6, 14615] [6, 14617] [6, 14620] [6, 14621] [6, 14624] [6, 14628] [6, 14630] [6, 14632] [6, 14634] [6, 14635] [6, 14637] [6, 14639] [6, 14640] [6, 14644] [6, 14646] [6, 14648] [6, 14653] [6, 14657] [6, 14660] [6, 14662] [6, 14664] [6, 14666] [6, 14670] [6, 14673] [6, 14674] [6, 14677] [6, 14687] [6, 14693] [6, 14695] [6, 14697] [6, 14698] [6, 14701] [6, 14704] [6, 14716] [6, 14719] [6, 14739] [6, 14741] [6, 14743] [6, 14744] [6, 14746] [6, 14748] [6, 14749] [6, 14753] [6, 14755] [6, 14757] [6, 14765] [6, 14766] [6, 14767] [6, 14768] [6, 14771] [6, 14774] [6, 14778] [6, 14783] [6, 14785] [6, 14788] [6, 14790] [6, 14792] [6, 14793] [6, 14803] [6, 14808] [6, 14810] [6, 14811] [6, 14828] [6, 14830] [6, 14840] [6, 14844] [6, 14849]
The identities
- x ≈ x³
- xyz ≈ xzy