A certified basis of 20 identities
This list of identities is a basis, proved in Lean, of 39 semigroups of order six, all of which generate the variety V[4042]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-2edbf61e3221a20c in the data of the bases-min seal.
Certified for
[6, 4042] [6, 4043] [6, 4051] [6, 4068] [6, 4072] [6, 4082] [6, 4086] [6, 4087] [6, 4176] [6, 4177] [6, 4181] [6, 4192] [6, 4196] [6, 6088] [6, 6089] [6, 6115] [6, 6314] [6, 6324] [6, 6384] [6, 6395] [6, 6396] [6, 6459] [6, 6803] [6, 6809] [6, 8841] [6, 8845] [6, 8857] [6, 8896] [6, 9919] [6, 10812] [6, 10822] [6, 10952] [6, 10953] [6, 10962] [6, 10968] [6, 10969] [6, 11231] [6, 11675] [6, 11775]
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x²yx ≈ xyx²
- x²yx ≈ yxy²
- x²yx² ≈ xyx
- x²yxy ≈ yxy
- x²y²x ≈ yxy
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- xyx ≈ yx²y²
- xyx ≈ yxyxy
- xyx ≈ yxy²x
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- xyzx ≈ xzyx
- x²yzx ≈ yxyzy
- xyxzy ≈ xy²zx
- xyxzy ≈ yx²zy