A certified basis of 12 identities
This list of identities is a basis, proved in Lean, of 28 semigroups of order six, all of which generate the variety V[7585]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-42e404f08584b2fd in the data of the bases-min seal.
Certified for
[6, 7585] [6, 7586] [6, 7587] [6, 7617] [6, 8173] [6, 8174] [6, 8184] [6, 8313] [6, 8314] [6, 8323] [6, 8371] [6, 8376] [6, 8408] [6, 8420] [6, 8481] [6, 8482] [6, 11205] [6, 11206] [6, 11207] [6, 11208] [6, 11500] [6, 13207] [6, 13237] [6, 13253] [6, 13383] [6, 13384] [6, 13611] [6, 13974]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- xyxzx ≈ xyzx
- xyxzy ≈ yx²zy
- xyzxy ≈ xyzyx
- xyzxy ≈ yxzxy
- xyzxz ≈ xyz²x
- xyzxty ≈ yxzxty
- xyztxz ≈ xyztzx