A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 69 semigroups of order six, all of which generate the variety V[2740]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-3ee5f87661124805 in the data of the bases-min seal.
Certified for
[6, 2740] [6, 2752] [6, 2759] [6, 2762] [6, 2763] [6, 2765] [6, 2767] [6, 2768] [6, 2769] [6, 2774] [6, 2775] [6, 2776] [6, 2777] [6, 2780] [6, 2781] [6, 2782] [6, 2786] [6, 2787] [6, 2788] [6, 2790] [6, 2791] [6, 2793] [6, 2794] [6, 5210] [6, 5221] [6, 5231] [6, 5232] [6, 5233] [6, 5234] [6, 5238] [6, 5239] [6, 5242] [6, 5244] [6, 5245] [6, 5246] [6, 5249] [6, 5251] [6, 5253] [6, 5254] [6, 5255] [6, 5256] [6, 5257] [6, 5258] [6, 5259] [6, 5260] [6, 5262] [6, 5354] [6, 5356] [6, 5460] [6, 5638] [6, 5639] [6, 5674] [6, 5711] [6, 9297] [6, 9298] [6, 9302] [6, 9303] [6, 9304] [6, 9305] [6, 9308] [6, 9310] [6, 9311] [6, 9312] [6, 9378] [6, 9440] [6, 9441] [6, 9460] [6, 9480] [6, 9577]
The identities
- x³ ≈ x⁴
- x²y ≈ xyx
- xyx ≈ yx²