A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 146 semigroups of order six, all of which generate the variety V[976]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-f8680aa7f5415c56 in the data of the bases-min seal.
Certified for
[6, 976] [6, 978] [6, 980] [6, 982] [6, 984] [6, 986] [6, 1001] [6, 1002] [6, 1011] [6, 1012] [6, 1017] [6, 1020] [6, 1021] [6, 1024] [6, 1025] [6, 1035] [6, 1082] [6, 2940] [6, 2944] [6, 2948] [6, 2970] [6, 2991] [6, 3245] [6, 3247] [6, 3249] [6, 3252] [6, 3254] [6, 3256] [6, 3270] [6, 3272] [6, 3274] [6, 3276] [6, 3284] [6, 3286] [6, 3288] [6, 3294] [6, 3296] [6, 3320] [6, 3322] [6, 3329] [6, 3332] [6, 3340] [6, 3343] [6, 3352] [6, 3381] [6, 3383] [6, 3394] [6, 3402] [6, 3407] [6, 3430] [6, 3432] [6, 3572] [6, 3963] [6, 3965] [6, 3967] [6, 3973] [6, 3977] [6, 5801] [6, 5905] [6, 5907] [6, 5909] [6, 5915] [6, 5943] [6, 5945] [6, 5968] [6, 5970] [6, 5989] [6, 6049] [6, 6050] [6, 6054] [6, 6058] [6, 6059] [6, 6092] [6, 6094] [6, 6096] [6, 6097] [6, 6100] [6, 6212] [6, 6216] [6, 6217] [6, 6259] [6, 6260] [6, 6267] [6, 6628] [6, 6650] [6, 6652] [6, 6654] [6, 6658] [6, 6660] [6, 6662] [6, 6667] [6, 6668] [6, 6679] [6, 7292] [6, 7295] [6, 7303] [6, 7305] [6, 7320] [6, 7328] [6, 7330] [6, 7344] [6, 7355] [6, 7358] [6, 7370] [6, 7372] [6, 7454] [6, 7460] [6, 7462] [6, 7551] [6, 7560] [6, 7567] [6, 7599] [6, 7602] [6, 7707] [6, 7710] [6, 8599] [6, 8602] [6, 8610] [6, 8612] [6, 8631] [6, 8721] [6, 8723] [6, 8766] [6, 9829] [6, 9863] [6, 10030] [6, 10033] [6, 10035] [6, 10037] [6, 10091] [6, 10094] [6, 10112] [6, 10114] [6, 10120] [6, 10125] [6, 10151] [6, 10255] [6, 10257] [6, 10286] [6, 10288] [6, 10299] [6, 10319] [6, 10322] [6, 11613] [6, 11630] [6, 11822]
The identities
- x² ≈ x³
- xyx ≈ yxy
- xy²z ≈ xyz