A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 117 semigroups of order six, all of which generate the variety V[2726]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-429d4e8c5d289020 in the data of the bases-min seal.
Certified for
[6, 2726] [6, 2731] [6, 2736] [6, 2743] [6, 2745] [6, 2749] [6, 2755] [6, 2757] [6, 2761] [6, 2766] [6, 2770] [6, 2783] [6, 2785] [6, 2789] [6, 2792] [6, 2795] [6, 5208] [6, 5212] [6, 5216] [6, 5219] [6, 5223] [6, 5227] [6, 5230] [6, 5235] [6, 5237] [6, 5243] [6, 5250] [6, 5252] [6, 5261] [6, 5263] [6, 5265] [6, 5342] [6, 5343] [6, 5351] [6, 5353] [6, 5355] [6, 5450] [6, 5454] [6, 5458] [6, 5462] [6, 5605] [6, 5607] [6, 5615] [6, 5617] [6, 5623] [6, 5624] [6, 5644] [6, 5645] [6, 5646] [6, 5650] [6, 5651] [6, 5655] [6, 5662] [6, 5664] [6, 5670] [6, 5672] [6, 5677] [6, 5706] [6, 5708] [6, 5710] [6, 5712] [6, 5870] [6, 9296] [6, 9299] [6, 9301] [6, 9309] [6, 9314] [6, 9318] [6, 9321] [6, 9376] [6, 9380] [6, 9384] [6, 9436] [6, 9437] [6, 9444] [6, 9446] [6, 9452] [6, 9453] [6, 9458] [6, 9462] [6, 9468] [6, 9471] [6, 9479] [6, 9481] [6, 9483] [6, 9514] [6, 9572] [6, 9573] [6, 9574] [6, 9576] [6, 9587] [6, 9590] [6, 9592] [6, 9598] [6, 9601] [6, 9602] [6, 9611] [6, 9620] [6, 9622] [6, 9650] [6, 9704] [6, 9705] [6, 9708] [6, 9711] [6, 9713] [6, 9714] [6, 9728] [6, 9730] [6, 9731] [6, 9740] [6, 9742] [6, 9754] [6, 9755] [6, 9758] [6, 9768] [6, 9770] [6, 9778]
The identities
- x³ ≈ x⁴
- xy ≈ yx