A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 342 semigroups of order six, all of which generate the variety V[963]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-14a0a7290e63f9fd in the data of the bases-min seal.
Certified for
[6, 963] [6, 964] [6, 965] [6, 966] [6, 967] [6, 968] [6, 969] [6, 970] [6, 971] [6, 972] [6, 973] [6, 2908] [6, 2911] [6, 2913] [6, 2916] [6, 2919] [6, 2922] [6, 3172] [6, 3173] [6, 3174] [6, 3175] [6, 3176] [6, 3177] [6, 3181] [6, 3182] [6, 3183] [6, 3184] [6, 3185] [6, 3186] [6, 3188] [6, 3189] [6, 3190] [6, 3192] [6, 3194] [6, 3195] [6, 3196] [6, 3201] [6, 3203] [6, 3205] [6, 3207] [6, 3208] [6, 3214] [6, 3216] [6, 3221] [6, 3223] [6, 3224] [6, 3225] [6, 3230] [6, 3232] [6, 3238] [6, 3955] [6, 3956] [6, 3957] [6, 3958] [6, 3959] [6, 3960] [6, 5773] [6, 5776] [6, 5779] [6, 5886] [6, 5887] [6, 5888] [6, 5889] [6, 5890] [6, 5891] [6, 5896] [6, 5898] [6, 5899] [6, 5900] [6, 5901] [6, 5902] [6, 5903] [6, 5934] [6, 5935] [6, 5936] [6, 5938] [6, 5939] [6, 5941] [6, 5942] [6, 5947] [6, 5949] [6, 5960] [6, 5962] [6, 5963] [6, 5965] [6, 5966] [6, 5972] [6, 5975] [6, 5984] [6, 5986] [6, 5987] [6, 5991] [6, 5992] [6, 5993] [6, 5995] [6, 6615] [6, 6617] [6, 6619] [6, 6641] [6, 6642] [6, 6643] [6, 6644] [6, 6645] [6, 6646] [6, 6647] [6, 6708] [6, 6709] [6, 6710] [6, 7056] [6, 7057] [6, 7058] [6, 7062] [6, 7063] [6, 7064] [6, 7066] [6, 7068] [6, 7070] [6, 7075] [6, 7077] [6, 7082] [6, 7089] [6, 7090] [6, 7091] [6, 7092] [6, 7094] [6, 7095] [6, 7096] [6, 7097] [6, 7099] [6, 7100] [6, 7101] [6, 7103] [6, 7124] [6, 7125] [6, 7126] [6, 7129] [6, 7130] [6, 7131] [6, 7140] [6, 7141] [6, 7143] [6, 7146] [6, 7148] [6, 7151] [6, 7171] [6, 7177] [6, 7186] [6, 7188] [6, 7189] [6, 7191] [6, 7197] [6, 7229] [6, 7231] [6, 7233] [6, 7235] [6, 7242] [6, 7267] [6, 7269] [6, 8566] [6, 8567] [6, 8568] [6, 8572] [6, 8573] [6, 8574] [6, 8576] [6, 8578] [6, 8580] [6, 8585] [6, 8587] [6, 8592] [6, 8699] [6, 8701] [6, 8703] [6, 8705] [6, 8707] [6, 8709] [6, 8751] [6, 8754] [6, 8757] [6, 9810] [6, 9812] [6, 9820] [6, 9823] [6, 9825] [6, 9858] [6, 9860] [6, 9980] [6, 9981] [6, 9985] [6, 9986] [6, 9989] [6, 9995] [6, 10003] [6, 10005] [6, 10006] [6, 10008] [6, 10009] [6, 10010] [6, 10011] [6, 10012] [6, 10014] [6, 10015] [6, 10016] [6, 10018] [6, 10050] [6, 10053] [6, 10059] [6, 10061] [6, 10062] [6, 10065] [6, 10066] [6, 10067] [6, 10070] [6, 10071] [6, 10073] [6, 10083] [6, 10085] [6, 10087] [6, 10134] [6, 10140] [6, 10144] [6, 10161] [6, 10236] [6, 10238] [6, 10245] [6, 10246] [6, 10248] [6, 10249] [6, 10263] [6, 10265] [6, 10271] [6, 10272] [6, 10274] [6, 10276] [6, 10280] [6, 10306] [6, 10309] [6, 10311] [6, 10314] [6, 10329] [6, 10333] [6, 10337] [6, 10338] [6, 10340] [6, 10343] [6, 10352] [6, 11604] [6, 11605] [6, 11608] [6, 11610] [6, 11611] [6, 11625] [6, 11627] [6, 11628] [6, 11632] [6, 11634] [6, 11716] [6, 11718] [6, 11744] [6, 11819] [6, 11820] [6, 11825] [6, 11938] [6, 11942] [6, 11945] [6, 11952] [6, 11953] [6, 11955] [6, 11968] [6, 11971] [6, 11976] [6, 11996] [6, 11998] [6, 12021] [6, 12022] [6, 12023] [6, 12030] [6, 12034] [6, 12036] [6, 12041] [6, 12042] [6, 12059] [6, 12063] [6, 12064] [6, 12111] [6, 12112] [6, 12115] [6, 12117] [6, 12122] [6, 12123] [6, 12126] [6, 12203] [6, 12206] [6, 12213] [6, 12217] [6, 12224] [6, 12226] [6, 12233] [6, 12236] [6, 12241] [6, 12263] [6, 12265] [6, 12402] [6, 12404] [6, 12410] [6, 12417] [6, 12419] [6, 13807] [6, 13811] [6, 13814] [6, 13821] [6, 13822] [6, 13824] [6, 13837] [6, 13840] [6, 13845] [6, 13865] [6, 13867] [6, 14017] [6, 14019] [6, 14026] [6, 14036] [6, 14038] [6, 14044] [6, 14061] [6, 14063] [6, 14067] [6, 14184] [6, 14197] [6, 14210] [6, 14300] [6, 14302] [6, 14308] [6, 14312] [6, 14316] [6, 14318] [6, 14392] [6, 14397] [6, 14399] [6, 14404] [6, 14443] [6, 14445]
The identities
- x² ≈ x³
- x²y ≈ xy
- xyx ≈ xy²
- xyx ≈ yx²