A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 271 semigroups of order six, all of which generate the variety V[3187]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-e9e2ae6b59000b51 in the data of the bases-min seal.
Certified for
[6, 3187] [6, 4006] [6, 5918] [6, 6012] [6, 6720] [6, 7065] [6, 7105] [6, 7121] [6, 7132] [6, 7154] [6, 7155] [6, 7165] [6, 7166] [6, 7168] [6, 7169] [6, 7289] [6, 8575] [6, 8698] [6, 8750] [6, 8761] [6, 8782] [6, 8788] [6, 8790] [6, 8794] [6, 8796] [6, 8797] [6, 8798] [6, 9833] [6, 9987] [6, 10020] [6, 10048] [6, 10057] [6, 10068] [6, 10133] [6, 10137] [6, 10162] [6, 10163] [6, 10166] [6, 10168] [6, 10169] [6, 10170] [6, 10171] [6, 10429] [6, 10441] [6, 10449] [6, 10452] [6, 10453] [6, 10454] [6, 10458] [6, 10468] [6, 10649] [6, 10665] [6, 10674] [6, 11616] [6, 11644] [6, 11711] [6, 11741] [6, 11751] [6, 11840] [6, 11943] [6, 11957] [6, 11965] [6, 11972] [6, 11979] [6, 11980] [6, 11984] [6, 11985] [6, 11987] [6, 11988] [6, 12018] [6, 12025] [6, 12038] [6, 12045] [6, 12046] [6, 12050] [6, 12052] [6, 12076] [6, 12081] [6, 12084] [6, 12085] [6, 12086] [6, 12094] [6, 12106] [6, 12108] [6, 12130] [6, 12137] [6, 12141] [6, 12142] [6, 12144] [6, 12145] [6, 12148] [6, 12149] [6, 12176] [6, 12179] [6, 12180] [6, 12187] [6, 12190] [6, 12191] [6, 12199] [6, 12200] [6, 12207] [6, 12219] [6, 12228] [6, 12237] [6, 12244] [6, 12245] [6, 12250] [6, 12273] [6, 12274] [6, 12279] [6, 12280] [6, 12286] [6, 12287] [6, 12301] [6, 12302] [6, 12303] [6, 12304] [6, 12305] [6, 12306] [6, 12308] [6, 12316] [6, 12317] [6, 12318] [6, 12319] [6, 12327] [6, 12328] [6, 12329] [6, 12330] [6, 12332] [6, 12333] [6, 12334] [6, 12336] [6, 12337] [6, 12339] [6, 12340] [6, 12341] [6, 12342] [6, 12346] [6, 12347] [6, 12348] [6, 12349] [6, 12352] [6, 12353] [6, 12500] [6, 12501] [6, 12506] [6, 12508] [6, 12511] [6, 12517] [6, 12521] [6, 12522] [6, 12523] [6, 12527] [6, 13812] [6, 13826] [6, 13834] [6, 13841] [6, 13848] [6, 13849] [6, 13853] [6, 13854] [6, 13856] [6, 13857] [6, 13887] [6, 14016] [6, 14029] [6, 14033] [6, 14041] [6, 14043] [6, 14047] [6, 14048] [6, 14050] [6, 14051] [6, 14053] [6, 14085] [6, 14183] [6, 14188] [6, 14193] [6, 14195] [6, 14200] [6, 14201] [6, 14225] [6, 14230] [6, 14282] [6, 14286] [6, 14288] [6, 14291] [6, 14292] [6, 14294] [6, 14296] [6, 14297] [6, 14298] [6, 14299] [6, 14330] [6, 14335] [6, 14381] [6, 14383] [6, 14387] [6, 14388] [6, 14389] [6, 14391] [6, 14407] [6, 14409] [6, 14417] [6, 14438] [6, 14440] [6, 14441] [6, 14442] [6, 14454] [6, 14456] [6, 14459] [6, 14460] [6, 14479] [6, 14484] [6, 14488] [6, 14493] [6, 14495] [6, 14496] [6, 14497] [6, 14498] [6, 14500] [6, 14501] [6, 14507] [6, 14515] [6, 14517] [6, 14519] [6, 14521] [6, 14523] [6, 14524] [6, 14526] [6, 14528] [6, 14533] [6, 14541] [6, 14542] [6, 14544] [6, 14546] [6, 14549] [6, 14553] [6, 14555] [6, 14556] [6, 14557] [6, 14558] [6, 14560] [6, 14562] [6, 14565] [6, 14566] [6, 14567] [6, 14569] [6, 14571] [6, 14573] [6, 14575] [6, 14577] [6, 14579] [6, 14583] [6, 14585] [6, 14586] [6, 14587] [6, 14588] [6, 14590] [6, 14591] [6, 14592] [6, 14593] [6, 14595] [6, 14597] [6, 14599] [6, 14600] [6, 14601] [6, 14602] [6, 14603] [6, 14605] [6, 14606]
The identities
- x² ≈ x³
- x²y ≈ xy
- xy ≈ xyx