A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 30 semigroups of order six, all of which generate the variety V[7644]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-13a9589a33eeabca in the data of the bases-min seal.
Certified for
[6, 7644] [6, 7664] [6, 8347] [6, 8356] [6, 8447] [6, 8461] [6, 8471] [6, 8493] [6, 10633] [6, 11261] [6, 11267] [6, 11481] [6, 12752] [6, 12771] [6, 13125] [6, 13226] [6, 13270] [6, 13278] [6, 13292] [6, 13454] [6, 13522] [6, 13705] [6, 13713] [6, 13717] [6, 13792] [6, 13805] [6, 13993] [6, 14149] [6, 14180] [6, 14256]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²yz ≈ xyxz
- xyzx ≈ xzyx
- xyzy ≈ xzy²
- xyzt ≈ xzyt