A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 58 semigroups of order six, all of which generate the variety V[7438]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-d417275d43f933d9 in the data of the bases-min seal.
Certified for
[6, 7438] [6, 7439] [6, 7502] [6, 7591] [6, 7594] [6, 7620] [6, 7825] [6, 7826] [6, 7853] [6, 7985] [6, 8030] [6, 8058] [6, 8272] [6, 8318] [6, 8321] [6, 8326] [6, 8411] [6, 8418] [6, 8423] [6, 8489] [6, 8490] [6, 8545] [6, 8551] [6, 10924] [6, 10925] [6, 10935] [6, 10943] [6, 10944] [6, 11212] [6, 11215] [6, 11225] [6, 11354] [6, 11501] [6, 12581] [6, 12644] [6, 12748] [6, 12766] [6, 12836] [6, 12853] [6, 12999] [6, 13001] [6, 13017] [6, 13021] [6, 13027] [6, 13054] [6, 13210] [6, 13256] [6, 13299] [6, 13389] [6, 13393] [6, 13424] [6, 13426] [6, 13434] [6, 13617] [6, 13620] [6, 13622] [6, 13941] [6, 13977]
The identities
- x² ≈ x³
- xyx ≈ yx²
- x²y²z ≈ xy²xz