A certified basis of 15 identities
This list of identities is a basis, proved in Lean, of 11 semigroups of order six, all of which generate the variety V[2999]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-65f4a75781ca44af in the data of the bases-min seal.
Certified for
[6, 2999] [6, 3035] [6, 3043] [6, 3092] [6, 3154] [6, 5815] [6, 5817] [6, 6535] [6, 6542] [6, 6596] [6, 6638]
The identities
- x² ≈ x⁴
- x²y ≈ yx²
- x³yx ≈ xyx
- x²y² ≈ xyxy
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- x²yzy ≈ xyxzy
- xyxzy ≈ yx²zy
- xyxz² ≈ xyzxz
- xyzxy ≈ xyzyx
- xyzxy ≈ yxzxy
- xyzxz ≈ xyz²x
- xyxztz ≈ xyzxtz
- xyzxty ≈ yxzxty
- xyztxz ≈ xyztzx