A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 147 semigroups of order six, all of which generate the variety V[2592]. Removing the identities that follow from the others leaves 1 identity (Vampire); the variety page shows the shortest known basis.
Identifier sb-d0bb8aeef5d91fa8 in the data of the bases-min seal.
Certified for
[6, 2592] [6, 2598] [6, 2600] [6, 2602] [6, 2620] [6, 2626] [6, 2628] [6, 2630] [6, 2632] [6, 2641] [6, 2642] [6, 2644] [6, 2646] [6, 2648] [6, 2650] [6, 2652] [6, 2655] [6, 2657] [6, 2661] [6, 2663] [6, 2687] [6, 2688] [6, 2690] [6, 2691] [6, 2693] [6, 2694] [6, 2696] [6, 2697] [6, 2698] [6, 2699] [6, 2701] [6, 2710] [6, 2712] [6, 2714] [6, 2715] [6, 2717] [6, 2719] [6, 2721] [6, 2722] [6, 2723] [6, 2725] [6, 5124] [6, 5130] [6, 5132] [6, 5134] [6, 5136] [6, 5141] [6, 5143] [6, 5145] [6, 5147] [6, 5149] [6, 5151] [6, 5153] [6, 5155] [6, 5165] [6, 5166] [6, 5168] [6, 5170] [6, 5171] [6, 5172] [6, 5173] [6, 5175] [6, 5177] [6, 5179] [6, 5181] [6, 5183] [6, 5185] [6, 5187] [6, 5189] [6, 5191] [6, 5192] [6, 5193] [6, 5194] [6, 5195] [6, 5197] [6, 5198] [6, 5199] [6, 5201] [6, 5203] [6, 5205] [6, 5333] [6, 5335] [6, 5336] [6, 5338] [6, 5340] [6, 5341] [6, 5383] [6, 5391] [6, 5393] [6, 5399] [6, 5404] [6, 5407] [6, 5409] [6, 5414] [6, 5419] [6, 5428] [6, 5429] [6, 5435] [6, 5439] [6, 5440] [6, 5442] [6, 5445] [6, 5447] [6, 5534] [6, 5543] [6, 5583] [6, 5591] [6, 5850] [6, 5851] [6, 5852] [6, 5855] [6, 5856] [6, 9268] [6, 9270] [6, 9272] [6, 9274] [6, 9276] [6, 9278] [6, 9279] [6, 9281] [6, 9283] [6, 9284] [6, 9286] [6, 9288] [6, 9290] [6, 9291] [6, 9293] [6, 9295] [6, 9343] [6, 9347] [6, 9353] [6, 9357] [6, 9359] [6, 9362] [6, 9364] [6, 9369] [6, 9373] [6, 9375] [6, 9414] [6, 9422] [6, 9433] [6, 9510] [6, 9511] [6, 9513] [6, 9543] [6, 9566] [6, 9698]
The identities
- x³ ≈ x²y
- x³ ≈ xyx
- x³ ≈ xy²
- x³ ≈ xyz