A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 48 semigroups of order six, all of which generate the variety V[3471]. Removing the identities that follow from the others leaves 5 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-a86475960551b00b in the data of the bases-min seal.
Certified for
[6, 3475] [6, 3477] [6, 3499] [6, 3680] [6, 3682] [6, 3694] [6, 3702] [6, 3752] [6, 3757] [6, 3758] [6, 3759] [6, 3761] [6, 3796] [6, 6082] [6, 6084] [6, 6112] [6, 6309] [6, 6311] [6, 6321] [6, 6367] [6, 6375] [6, 6376] [6, 6379] [6, 6380] [6, 6381] [6, 6391] [6, 6474] [6, 6521] [6, 6582] [6, 7887] [6, 7905] [6, 7928] [6, 8012] [6, 8014] [6, 8372] [6, 8412] [6, 8660] [6, 9914] [6, 10864] [6, 10866] [6, 10893] [6, 10895] [6, 10909] [6, 10932] [6, 10938] [6, 11216] [6, 11219] [6, 11672]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- xyzy ≈ xzy²
- xyxzx ≈ xyzx