A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 64 semigroups of order six, all of which generate the variety V[15012]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-3afed8c697821712 in the data of the bases-min seal.
Certified for
[6, 15012] [6, 15031] [6, 15044] [6, 15062] [6, 15064] [6, 15075] [6, 15087] [6, 15097] [6, 15114] [6, 15140] [6, 15180] [6, 15186] [6, 15189] [6, 15194] [6, 15238] [6, 15240] [6, 15241] [6, 15246] [6, 15261] [6, 15285] [6, 15303] [6, 15325] [6, 15327] [6, 15343] [6, 15366] [6, 15369] [6, 15376] [6, 15399] [6, 15403] [6, 15430] [6, 15461] [6, 15477] [6, 15495] [6, 15526] [6, 15528] [6, 15536] [6, 15544] [6, 15551] [6, 15583] [6, 15592] [6, 15596] [6, 15603] [6, 15622] [6, 15625] [6, 15630] [6, 15632] [6, 15634] [6, 15653] [6, 15671] [6, 15689] [6, 15702] [6, 15716] [6, 15727] [6, 15737] [6, 15746] [6, 15762] [6, 15782] [6, 15821] [6, 15855] [6, 15859] [6, 15861] [6, 15866] [6, 15868] [6, 15873]
The identities
- x ≈ x²
- xyzx ≈ xzyx