A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 64 semigroups of order six, all of which generate the variety V[4055]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-5facf9148ff03ab2 in the data of the bases-min seal.
Certified for
[6, 4055] [6, 4093] [6, 4100] [6, 4102] [6, 4159] [6, 4202] [6, 4210] [6, 4267] [6, 4299] [6, 4306] [6, 4308] [6, 6208] [6, 6491] [6, 6518] [6, 6523] [6, 6534] [6, 6604] [6, 6819] [6, 6843] [6, 6898] [6, 6962] [6, 6986] [6, 7041] [6, 8848] [6, 8851] [6, 8869] [6, 8872] [6, 8880] [6, 8882] [6, 8884] [6, 8899] [6, 8911] [6, 8996] [6, 8999] [6, 9013] [6, 9016] [6, 9022] [6, 9024] [6, 9026] [6, 9040] [6, 9052] [6, 9889] [6, 9932] [6, 9934] [6, 9948] [6, 10816] [6, 10826] [6, 11151] [6, 11190] [6, 11193] [6, 11360] [6, 11362] [6, 11364] [6, 11365] [6, 11369] [6, 11373] [6, 11511] [6, 11515] [6, 11592] [6, 11595] [6, 11695] [6, 11737] [6, 11779] [6, 11784]
The identities
- x² ≈ x⁴
- x²y ≈ xyx
- xyz ≈ xzy