A certified basis of 25 identities
This list of identities is a basis, proved in Lean, of 58 semigroups of order six, all of which generate the variety V[4040]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-0f13b4b66a49655f in the data of the bases-min seal.
Certified for
[6, 4040] [6, 4041] [6, 4050] [6, 4067] [6, 4071] [6, 4081] [6, 4085] [6, 4146] [6, 4147] [6, 4154] [6, 4174] [6, 4175] [6, 4180] [6, 4191] [6, 4195] [6, 4255] [6, 4256] [6, 4263] [6, 4279] [6, 4282] [6, 4290] [6, 4293] [6, 6086] [6, 6087] [6, 6114] [6, 6313] [6, 6323] [6, 6383] [6, 6393] [6, 6394] [6, 6457] [6, 6802] [6, 6808] [6, 6947] [6, 6952] [6, 8840] [6, 8844] [6, 8853] [6, 8855] [6, 8895] [6, 8990] [6, 8993] [6, 9001] [6, 9003] [6, 9037] [6, 9918] [6, 10811] [6, 10821] [6, 10831] [6, 10947] [6, 10948] [6, 10961] [6, 10965] [6, 10966] [6, 10974] [6, 11226] [6, 11674] [6, 11774]
The identities
- x² ≈ x⁴
- x³yx ≈ xyx
- x³y² ≈ yxy
- x²yx ≈ xyx²
- x²yx ≈ yxy²
- x²yx² ≈ xyx
- x²yxy ≈ yxy
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- x²y²x ≈ yxy
- x²y³ ≈ xyx
- xyx ≈ xyx³
- xyx ≈ xyxy²
- xyx ≈ xy²xy
- xyx ≈ xy³x
- xyx ≈ yx²y²
- xyx ≈ yxyxy
- xyx ≈ yxy²x
- xyzx ≈ xzyx
- x²yzx ≈ yxyzy
- x²yzy ≈ xyxzy
- x²yzy ≈ xy²zx
- x²yzy ≈ xzxy²
- x²yzy ≈ yx²zy