A certified basis of 7 identities
This list of identities is a basis, proved in Lean, of 44 semigroups of order six, all of which generate the variety V[2586]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-d8639966eb8336a8 in the data of the bases-min seal.
Certified for
[6, 2586] [6, 2587] [6, 2588] [6, 2589] [6, 2590] [6, 2591] [6, 2594] [6, 2595] [6, 2596] [6, 2597] [6, 2615] [6, 2616] [6, 2622] [6, 2623] [6, 2624] [6, 2625] [6, 5121] [6, 5122] [6, 5123] [6, 5126] [6, 5127] [6, 5128] [6, 5129] [6, 5138] [6, 5139] [6, 5140] [6, 5378] [6, 5379] [6, 5381] [6, 5388] [6, 5389] [6, 5390] [6, 5514] [6, 5515] [6, 5519] [6, 5520] [6, 5523] [6, 5529] [6, 5694] [6, 5695] [6, 9520] [6, 9614] [6, 9626] [6, 9627]
The identities
- x³ ≈ x⁴
- xyx ≈ xy²
- xyx ≈ yx²
- x³y ≈ x²y
- x²yx ≈ xyx
- xyz ≈ yxz
- x²yz ≈ xyz