A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 369 semigroups of order six, all of which generate the variety V[975]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-d33ce436aa320298 in the data of the bases-min seal.
Certified for
[6, 975] [6, 1015] [6, 1028] [6, 1078] [6, 1087] [6, 1105] [6, 1119] [6, 1120] [6, 1121] [6, 1125] [6, 1140] [6, 1147] [6, 1154] [6, 1158] [6, 1177] [6, 1179] [6, 1195] [6, 1201] [6, 1203] [6, 1207] [6, 2937] [6, 2978] [6, 2987] [6, 2997] [6, 3021] [6, 3031] [6, 3033] [6, 3041] [6, 3053] [6, 3062] [6, 3066] [6, 3244] [6, 3251] [6, 3324] [6, 3400] [6, 3405] [6, 3456] [6, 3460] [6, 3523] [6, 3538] [6, 3561] [6, 3584] [6, 3600] [6, 3628] [6, 3632] [6, 3664] [6, 3667] [6, 3724] [6, 3737] [6, 3745] [6, 3746] [6, 3781] [6, 3791] [6, 3846] [6, 3850] [6, 3856] [6, 3862] [6, 3867] [6, 3868] [6, 3880] [6, 3898] [6, 3908] [6, 3919] [6, 3923] [6, 3927] [6, 3935] [6, 3951] [6, 3962] [6, 3975] [6, 3980] [6, 3986] [6, 3990] [6, 3993] [6, 3998] [6, 5798] [6, 5807] [6, 5813] [6, 5904] [6, 6048] [6, 6053] [6, 6056] [6, 6062] [6, 6199] [6, 6203] [6, 6247] [6, 6252] [6, 6255] [6, 6287] [6, 6289] [6, 6292] [6, 6296] [6, 6352] [6, 6353] [6, 6354] [6, 6356] [6, 6446] [6, 6451] [6, 6452] [6, 6464] [6, 6466] [6, 6485] [6, 6487] [6, 6526] [6, 6528] [6, 6546] [6, 6553] [6, 6558] [6, 6561] [6, 6576] [6, 6578] [6, 6585] [6, 6590] [6, 6593] [6, 6594] [6, 6626] [6, 6632] [6, 6636] [6, 6649] [6, 6665] [6, 6671] [6, 6683] [6, 6687] [6, 6696] [6, 6698] [6, 6712] [6, 6717] [6, 6718] [6, 6730] [6, 6740] [6, 6746] [6, 6750] [6, 6752] [6, 6755] [6, 6758] [6, 6759] [6, 7291] [6, 7294] [6, 7319] [6, 7343] [6, 7354] [6, 7357] [6, 7548] [6, 7558] [6, 7564] [6, 7692] [6, 7695] [6, 7732] [6, 7734] [6, 7750] [6, 7765] [6, 7771] [6, 7773] [6, 7882] [6, 7883] [6, 7901] [6, 7918] [6, 7922] [6, 7923] [6, 8094] [6, 8098] [6, 8102] [6, 8160] [6, 8163] [6, 8166] [6, 8237] [6, 8256] [6, 8257] [6, 8296] [6, 8302] [6, 8305] [6, 8364] [6, 8366] [6, 8368] [6, 8401] [6, 8403] [6, 8405] [6, 8479] [6, 8483] [6, 8510] [6, 8513] [6, 8535] [6, 8536] [6, 8547] [6, 8555] [6, 8557] [6, 8598] [6, 8601] [6, 8628] [6, 8637] [6, 8639] [6, 8655] [6, 8656] [6, 8674] [6, 8678] [6, 8683] [6, 8689] [6, 8692] [6, 8717] [6, 8719] [6, 8731] [6, 8733] [6, 8745] [6, 8747] [6, 8764] [6, 8771] [6, 8776] [6, 9827] [6, 9891] [6, 9893] [6, 9895] [6, 9899] [6, 9938] [6, 9943] [6, 10029] [6, 10032] [6, 10090] [6, 10093] [6, 10122] [6, 10147] [6, 10687] [6, 10688] [6, 10697] [6, 10698] [6, 10707] [6, 10709] [6, 10725] [6, 10726] [6, 10744] [6, 10747] [6, 10749] [6, 10750] [6, 10752] [6, 10767] [6, 10768] [6, 10783] [6, 10786] [6, 10790] [6, 10793] [6, 10796] [6, 10802] [6, 10807] [6, 11171] [6, 11173] [6, 11175] [6, 11177] [6, 11178] [6, 11179] [6, 11185] [6, 11187] [6, 11324] [6, 11326] [6, 11332] [6, 11338] [6, 11344] [6, 11347] [6, 11463] [6, 11466] [6, 11473] [6, 11474] [6, 11479] [6, 11483] [6, 11492] [6, 11497] [6, 11498] [6, 11555] [6, 11558] [6, 11569] [6, 11570] [6, 11580] [6, 11582] [6, 11585] [6, 11586] [6, 11588] [6, 11612] [6, 11661] [6, 11662] [6, 11663] [6, 11665] [6, 11689] [6, 11691] [6, 11701] [6, 11704] [6, 11705] [6, 11732] [6, 11734] [6, 11754] [6, 11821] [6, 11833] [6, 11834] [6, 12529] [6, 12530] [6, 12539] [6, 12547] [6, 12549] [6, 12550] [6, 12603] [6, 12611] [6, 12615] [6, 12616] [6, 12661] [6, 12662] [6, 12699] [6, 12784] [6, 12786] [6, 12797] [6, 12798] [6, 12804] [6, 12809] [6, 12811] [6, 12812] [6, 13201] [6, 13203] [6, 13204] [6, 13234] [6, 13235] [6, 13250] [6, 13274] [6, 13279] [6, 13280] [6, 13283] [6, 13285] [6, 13286] [6, 13591] [6, 13593] [6, 13597] [6, 13598] [6, 13601] [6, 13603] [6, 13605] [6, 13780] [6, 13782] [6, 13787] [6, 13794] [6, 13796] [6, 13889] [6, 13890] [6, 13899] [6, 13907] [6, 13909] [6, 13910] [6, 13968] [6, 13970] [6, 13971] [6, 14007] [6, 14009] [6, 14095] [6, 14097] [6, 14100] [6, 14104] [6, 14106] [6, 14109] [6, 14170] [6, 14172] [6, 14176] [6, 14233] [6, 14235] [6, 14273] [6, 14356] [6, 14358] [6, 14363] [6, 14367] [6, 14371] [6, 14373] [6, 14425] [6, 14429] [6, 14431] [6, 14435] [6, 14469] [6, 14471]
The identities
- x² ≈ x³
- xy ≈ yx