A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 111 semigroups of order six, all of which generate the variety V[4044]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-5ce0173202ca94cd in the data of the bases-min seal.
Certified for
[6, 4044] [6, 4045] [6, 4052] [6, 4069] [6, 4070] [6, 4073] [6, 4078] [6, 4080] [6, 4083] [6, 4090] [6, 4099] [6, 4148] [6, 4149] [6, 4155] [6, 4178] [6, 4179] [6, 4182] [6, 4186] [6, 4190] [6, 4193] [6, 4200] [6, 4208] [6, 4257] [6, 4258] [6, 4264] [6, 4280] [6, 4281] [6, 4283] [6, 4287] [6, 4289] [6, 4291] [6, 4296] [6, 4305] [6, 6090] [6, 6091] [6, 6116] [6, 6210] [6, 6236] [6, 6238] [6, 6315] [6, 6316] [6, 6325] [6, 6371] [6, 6386] [6, 6397] [6, 6398] [6, 6476] [6, 6493] [6, 6504] [6, 6505] [6, 6538] [6, 6539] [6, 6540] [6, 6551] [6, 6584] [6, 6588] [6, 6804] [6, 6805] [6, 6807] [6, 6810] [6, 6813] [6, 6816] [6, 6902] [6, 6948] [6, 6949] [6, 6951] [6, 6953] [6, 6956] [6, 6959] [6, 7045] [6, 8842] [6, 8846] [6, 8854] [6, 8859] [6, 8860] [6, 8875] [6, 8897] [6, 8991] [6, 8994] [6, 9002] [6, 9005] [6, 9006] [6, 9018] [6, 9038] [6, 9911] [6, 9913] [6, 9917] [6, 9920] [6, 9921] [6, 9922] [6, 10813] [6, 10823] [6, 10832] [6, 10957] [6, 10958] [6, 10963] [6, 10964] [6, 10971] [6, 10972] [6, 10975] [6, 11235] [6, 11367] [6, 11374] [6, 11379] [6, 11383] [6, 11387] [6, 11517] [6, 11523] [6, 11676] [6, 11697] [6, 11776]
The identities
- x² ≈ x⁴
- xyx ≈ yx²
- x²y² ≈ y²x²