A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 39 semigroups of order six, all of which generate the variety V[6197]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-582f245446b17696 in the data of the bases-min seal.
Certified for
[6, 6197] [6, 6483] [6, 6514] [6, 6600] [6, 6842] [6, 6879] [6, 6985] [6, 7022] [6, 8909] [6, 9050] [6, 9850] [6, 9927] [6, 10815] [6, 10825] [6, 10834] [6, 10839] [6, 10844] [6, 11146] [6, 11150] [6, 11298] [6, 11305] [6, 11309] [6, 11314] [6, 11315] [6, 11318] [6, 11319] [6, 11320] [6, 11321] [6, 11409] [6, 11416] [6, 11452] [6, 11456] [6, 11460] [6, 11461] [6, 11462] [6, 11545] [6, 11687] [6, 11731] [6, 11778]
The identities
- x² ≈ x⁴
- x²y ≈ xyx
- xy ≈ xy³