A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 372 semigroups of order six, all of which generate the variety V[3302]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-16e6a93a26834d97 in the data of the bases-min seal.
Certified for
[6, 3302] [6, 3442] [6, 3505] [6, 3654] [6, 3704] [6, 3767] [6, 6032] [6, 6118] [6, 6135] [6, 6193] [6, 6327] [6, 6339] [6, 6400] [6, 6414] [6, 6481] [6, 6511] [6, 6722] [6, 7311] [6, 7336] [6, 7377] [6, 7383] [6, 7387] [6, 7507] [6, 7515] [6, 7521] [6, 7522] [6, 7523] [6, 7537] [6, 7623] [6, 7632] [6, 7633] [6, 7638] [6, 7744] [6, 7760] [6, 7785] [6, 7790] [6, 7793] [6, 7858] [6, 7864] [6, 7869] [6, 7870] [6, 7871] [6, 7881] [6, 7893] [6, 7911] [6, 7932] [6, 7936] [6, 7940] [6, 8063] [6, 8071] [6, 8077] [6, 8078] [6, 8079] [6, 8093] [6, 8124] [6, 8141] [6, 8187] [6, 8194] [6, 8213] [6, 8279] [6, 8329] [6, 8336] [6, 8337] [6, 8341] [6, 8379] [6, 8384] [6, 8396] [6, 8426] [6, 8435] [6, 8436] [6, 8441] [6, 8618] [6, 8649] [6, 8666] [6, 8716] [6, 8730] [6, 8740] [6, 9834] [6, 9926] [6, 10040] [6, 10103] [6, 10146] [6, 10493] [6, 10501] [6, 10506] [6, 10508] [6, 10510] [6, 10538] [6, 10545] [6, 10565] [6, 10566] [6, 10567] [6, 10568] [6, 10572] [6, 10583] [6, 10586] [6, 10592] [6, 10599] [6, 10600] [6, 10605] [6, 10657] [6, 10693] [6, 10703] [6, 10718] [6, 10737] [6, 10791] [6, 10794] [6, 10798] [6, 10803] [6, 10808] [6, 10993] [6, 11003] [6, 11009] [6, 11012] [6, 11046] [6, 11047] [6, 11048] [6, 11052] [6, 11062] [6, 11070] [6, 11091] [6, 11096] [6, 11108] [6, 11129] [6, 11135] [6, 11142] [6, 11240] [6, 11248] [6, 11249] [6, 11278] [6, 11286] [6, 11290] [6, 11291] [6, 11292] [6, 11293] [6, 11294] [6, 11295] [6, 11296] [6, 11399] [6, 11407] [6, 11419] [6, 11429] [6, 11438] [6, 11440] [6, 11443] [6, 11448] [6, 11449] [6, 11450] [6, 11529] [6, 11537] [6, 11651] [6, 11678] [6, 11685] [6, 11729] [6, 12535] [6, 12544] [6, 12555] [6, 12557] [6, 12559] [6, 12586] [6, 12590] [6, 12594] [6, 12595] [6, 12596] [6, 12602] [6, 12608] [6, 12621] [6, 12623] [6, 12648] [6, 12651] [6, 12654] [6, 12655] [6, 12656] [6, 12673] [6, 12677] [6, 12679] [6, 12681] [6, 12695] [6, 12716] [6, 12720] [6, 12723] [6, 12725] [6, 12728] [6, 12729] [6, 12730] [6, 12742] [6, 12755] [6, 12756] [6, 12759] [6, 12777] [6, 12778] [6, 12783] [6, 12838] [6, 12840] [6, 12844] [6, 12846] [6, 12848] [6, 12849] [6, 12857] [6, 12858] [6, 12860] [6, 12862] [6, 12864] [6, 12866] [6, 12868] [6, 12869] [6, 12872] [6, 12873] [6, 12874] [6, 12875] [6, 12876] [6, 12879] [6, 12881] [6, 12887] [6, 12889] [6, 12892] [6, 12893] [6, 12894] [6, 13066] [6, 13070] [6, 13074] [6, 13075] [6, 13076] [6, 13077] [6, 13078] [6, 13086] [6, 13087] [6, 13089] [6, 13092] [6, 13093] [6, 13094] [6, 13099] [6, 13100] [6, 13102] [6, 13107] [6, 13111] [6, 13114] [6, 13117] [6, 13118] [6, 13122] [6, 13128] [6, 13129] [6, 13132] [6, 13139] [6, 13141] [6, 13142] [6, 13144] [6, 13145] [6, 13146] [6, 13147] [6, 13148] [6, 13149] [6, 13158] [6, 13159] [6, 13160] [6, 13213] [6, 13218] [6, 13219] [6, 13222] [6, 13240] [6, 13243] [6, 13248] [6, 13259] [6, 13263] [6, 13264] [6, 13300] [6, 13301] [6, 13307] [6, 13310] [6, 13311] [6, 13312] [6, 13318] [6, 13320] [6, 13321] [6, 13441] [6, 13446] [6, 13447] [6, 13450] [6, 13462] [6, 13464] [6, 13468] [6, 13471] [6, 13472] [6, 13475] [6, 13485] [6, 13486] [6, 13487] [6, 13494] [6, 13495] [6, 13496] [6, 13499] [6, 13502] [6, 13503] [6, 13504] [6, 13505] [6, 13506] [6, 13510] [6, 13511] [6, 13512] [6, 13515] [6, 13516] [6, 13542] [6, 13543] [6, 13546] [6, 13547] [6, 13625] [6, 13631] [6, 13635] [6, 13637] [6, 13638] [6, 13645] [6, 13646] [6, 13649] [6, 13670] [6, 13671] [6, 13673] [6, 13674] [6, 13677] [6, 13678] [6, 13686] [6, 13687] [6, 13691] [6, 13692] [6, 13695] [6, 13696] [6, 13742] [6, 13895] [6, 13904] [6, 13915] [6, 13917] [6, 13919] [6, 13946] [6, 13950] [6, 13954] [6, 13955] [6, 13956] [6, 13962] [6, 13980] [6, 13985] [6, 13986] [6, 13989] [6, 14094] [6, 14099] [6, 14103] [6, 14108] [6, 14130] [6, 14131] [6, 14132] [6, 14133] [6, 14134] [6, 14146] [6, 14148] [6, 14161] [6, 14165] [6, 14166] [6, 14245] [6, 14249] [6, 14250] [6, 14265] [6, 14344] [6, 14347] [6, 14349] [6, 14350] [6, 14351] [6, 14352] [6, 14353] [6, 14354] [6, 14355] [6, 14420] [6, 14422] [6, 14423] [6, 14424]
The identities
- xy ≈ xy²
- x²y ≈ xyx