A certified basis of 7 identities
This list of identities is a basis, proved in Lean, of 54 semigroups of order six, all of which generate the variety V[988]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-1576a732b7204cf1 in the data of the bases-min seal.
Certified for
[6, 988] [6, 1006] [6, 1056] [6, 1058] [6, 1060] [6, 1069] [6, 1076] [6, 1130] [6, 1132] [6, 1136] [6, 1209] [6, 1210] [6, 1212] [6, 1213] [6, 1214] [6, 1215] [6, 1216] [6, 1218] [6, 1219] [6, 1220] [6, 2905] [6, 2906] [6, 2927] [6, 2928] [6, 2929] [6, 2954] [6, 2955] [6, 2956] [6, 2957] [6, 2964] [6, 2965] [6, 2966] [6, 2981] [6, 2982] [6, 2984] [6, 3011] [6, 3012] [6, 3016] [6, 3017] [6, 3058] [6, 3359] [6, 3363] [6, 3969] [6, 4001] [6, 4007] [6, 5767] [6, 5768] [6, 5788] [6, 5789] [6, 5893] [6, 5911] [6, 5920] [6, 6613] [6, 9808]
The identities
- x² ≈ x³
- x²y ≈ xyx
- x²y ≈ xy²
- x²y ≈ yx²
- xyz ≈ xzy
- xyz ≈ yxz
- x²yz ≈ xyz