A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 97 semigroups of order six, all of which generate the variety V[7404]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-f6623f65cabfceab in the data of the bases-min seal.
Certified for
[6, 7404] [6, 7406] [6, 7422] [6, 7424] [6, 7487] [6, 7495] [6, 7589] [6, 7593] [6, 7619] [6, 7800] [6, 7802] [6, 7814] [6, 7816] [6, 7838] [6, 7846] [6, 7957] [6, 7959] [6, 7970] [6, 7999] [6, 8001] [6, 8016] [6, 8018] [6, 8022] [6, 8042] [6, 8050] [6, 8204] [6, 8210] [6, 8270] [6, 8316] [6, 8320] [6, 8325] [6, 8393] [6, 8410] [6, 8413] [6, 8417] [6, 8422] [6, 8488] [6, 8543] [6, 8550] [6, 10563] [6, 10860] [6, 10862] [6, 10868] [6, 10870] [6, 10888] [6, 10890] [6, 10892] [6, 10900] [6, 10902] [6, 10904] [6, 11031] [6, 11040] [6, 11102] [6, 11210] [6, 11214] [6, 11220] [6, 11224] [6, 11336] [6, 11341] [6, 11488] [6, 12566] [6, 12574] [6, 12629] [6, 12637] [6, 12668] [6, 12711] [6, 12737] [6, 12825] [6, 12833] [6, 12917] [6, 12920] [6, 12939] [6, 12941] [6, 12945] [6, 12987] [6, 12989] [6, 12991] [6, 12994] [6, 12997] [6, 13004] [6, 13209] [6, 13255] [6, 13298] [6, 13360] [6, 13361] [6, 13388] [6, 13392] [6, 13394] [6, 13395] [6, 13397] [6, 13614] [6, 13616] [6, 13619] [6, 13926] [6, 13934] [6, 13976] [6, 14122]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- xyzy ≈ xzy²
- xyxzx ≈ xyzx
- xyxz² ≈ xyz²x