A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 42 semigroups of order six, all of which generate the variety V[5521]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-f36c1f6ac300ea2f in the data of the bases-min seal.
Certified for
[6, 5521] [6, 5541] [6, 5576] [6, 5589] [6, 5726] [6, 5728] [6, 5731] [6, 9412] [6, 9420] [6, 9431] [6, 9491] [6, 9493] [6, 9495] [6, 9526] [6, 9529] [6, 9538] [6, 9559] [6, 9561] [6, 9564] [6, 9636] [6, 9669] [6, 9674] [6, 9678] [6, 9683] [6, 9685] [6, 9686] [6, 9687] [6, 9688] [6, 9690] [6, 9691] [6, 9697] [6, 9750] [6, 9763] [6, 9773] [6, 9775] [6, 9784] [6, 9789] [6, 9791] [6, 9795] [6, 9797] [6, 9798] [6, 9799]
The identities
- x³ ≈ x⁴
- x²y ≈ xyx
- x²y ≈ xy²
- x³y ≈ x²y
- x²yz ≈ xyz