A certified basis of 16 identities
This list of identities is a basis, proved in Lean, of 44 semigroups of order six, all of which generate the variety V[1110]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-e793af5ca9054cbc in the data of the bases-min seal.
Certified for
[6, 1110] [6, 1111] [6, 1112] [6, 1113] [6, 1114] [6, 1116] [6, 1122] [6, 1123] [6, 1124] [6, 1162] [6, 1163] [6, 1164] [6, 1165] [6, 1166] [6, 1168] [6, 1171] [6, 1172] [6, 1174] [6, 1180] [6, 1181] [6, 1182] [6, 1183] [6, 1185] [6, 1187] [6, 1188] [6, 1189] [6, 1192] [6, 3044] [6, 3046] [6, 3048] [6, 3800] [6, 3801] [6, 3802] [6, 3803] [6, 3817] [6, 3818] [6, 3937] [6, 3940] [6, 3946] [6, 3994] [6, 3995] [6, 3996] [6, 6357] [6, 6358]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- x²y² ≈ xy²x
- x²y² ≈ yx²y
- x²yzy ≈ x²zy²
- x²yzy ≈ xyxzy
- x²yzy ≈ xy²zx
- x²yzy ≈ xyzxy
- x²yzy ≈ xyzyx
- x²yzy ≈ xzxy²
- x²yzy ≈ xzyxy
- x²yzy ≈ xzy²x
- x²yzy ≈ yx²zy
- xyxzx ≈ xzxyx