A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 43 semigroups of order six, all of which generate the variety V[2603]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-38ccd059c2844b41 in the data of the bases-min seal.
Certified for
[6, 2603] [6, 2608] [6, 2666] [6, 2668] [6, 2673] [6, 2674] [6, 2678] [6, 2679] [6, 2681] [6, 2682] [6, 5156] [6, 5157] [6, 5160] [6, 5162] [6, 5163] [6, 5164] [6, 5420] [6, 5423] [6, 5424] [6, 5481] [6, 5485] [6, 5545] [6, 5546] [6, 5555] [6, 5556] [6, 5569] [6, 5571] [6, 5699] [6, 5700] [6, 5857] [6, 5860] [6, 5862] [6, 9394] [6, 9398] [6, 9522] [6, 9616] [6, 9629] [6, 9634] [6, 9646] [6, 9652] [6, 9655] [6, 9658] [6, 9659]
The identities
- x³ ≈ x⁴
- xy ≈ yx
- x³y ≈ x²y