A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 31 semigroups of order six, all of which generate the variety V[7674]. Removing the identities that follow from the others leaves 7 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-46cf5ed606898b3e in the data of the bases-min seal.
Certified for
[6, 7674] [6, 8231] [6, 8234] [6, 8499] [6, 8503] [6, 8504] [6, 10424] [6, 10640] [6, 10987] [6, 10990] [6, 11122] [6, 11125] [6, 11273] [6, 11551] [6, 13555] [6, 13558] [6, 13565] [6, 13567] [6, 13571] [6, 13572] [6, 13573] [6, 13750] [6, 13753] [6, 13754] [6, 13756] [6, 13765] [6, 13766] [6, 13767] [6, 13768] [6, 14003] [6, 14379]
The identities
- x² ≈ x³
- x²y ≈ x²yx
- xyx ≈ xyx²
- xyxy ≈ xy²x
- xyxz ≈ xyxzx
- xyzxy ≈ xyzyx
- xyzxz ≈ xyz²x
- xyztxz ≈ xyztzx