A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 82 semigroups of order six, all of which generate the variety V[7390]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-739e223647b1695d in the data of the bases-min seal.
Certified for
[6, 7390] [6, 7392] [6, 7394] [6, 7410] [6, 7411] [6, 7481] [6, 7483] [6, 7490] [6, 7575] [6, 7610] [6, 7794] [6, 7796] [6, 7805] [6, 7832] [6, 7834] [6, 7841] [6, 7944] [6, 7948] [6, 7993] [6, 7995] [6, 8004] [6, 8006] [6, 8036] [6, 8038] [6, 8045] [6, 8125] [6, 8146] [6, 8150] [6, 8241] [6, 10551] [6, 10553] [6, 10555] [6, 10848] [6, 10850] [6, 10874] [6, 11021] [6, 11024] [6, 11034] [6, 11036] [6, 11068] [6, 11076] [6, 11078] [6, 11195] [6, 11279] [6, 11400] [6, 12560] [6, 12562] [6, 12569] [6, 12625] [6, 12632] [6, 12664] [6, 12685] [6, 12687] [6, 12703] [6, 12735] [6, 12791] [6, 12822] [6, 12824] [6, 12830] [6, 12895] [6, 12897] [6, 12899] [6, 12900] [6, 12904] [6, 12924] [6, 12926] [6, 12929] [6, 12931] [6, 12972] [6, 12974] [6, 12977] [6, 13323] [6, 13324] [6, 13326] [6, 13332] [6, 13333] [6, 13368] [6, 13370] [6, 13920] [6, 13922] [6, 13929] [6, 14112]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- x²y² ≈ xyx
- xyzx ≈ xzyx
- xyzy ≈ xzyz