A certified basis of 24 identities
This list of identities is a basis, proved in Lean, of 114 semigroups of order six, all of which generate the variety V[7391]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-c01f805387d1a54d in the data of the bases-min seal.
Certified for
[6, 7391] [6, 7393] [6, 7432] [6, 7433] [6, 7444] [6, 7482] [6, 7499] [6, 7505] [6, 7795] [6, 7822] [6, 7831] [6, 7833] [6, 7850] [6, 7856] [6, 7945] [6, 7978] [6, 7992] [6, 7994] [6, 8026] [6, 8035] [6, 8037] [6, 8054] [6, 8061] [6, 8127] [6, 8136] [6, 8148] [6, 8155] [6, 10514] [6, 10515] [6, 10516] [6, 10533] [6, 10534] [6, 10552] [6, 10554] [6, 10849] [6, 10916] [6, 10946] [6, 11015] [6, 11017] [6, 11022] [6, 11035] [6, 11042] [6, 11063] [6, 11072] [6, 11077] [6, 11083] [6, 11280] [6, 11287] [6, 11402] [6, 12561] [6, 12578] [6, 12584] [6, 12626] [6, 12641] [6, 12686] [6, 12691] [6, 12693] [6, 12704] [6, 12736] [6, 12739] [6, 12746] [6, 12762] [6, 12781] [6, 12823] [6, 12827] [6, 12842] [6, 12852] [6, 12859] [6, 12896] [6, 12898] [6, 12901] [6, 12902] [6, 12903] [6, 12905] [6, 12925] [6, 12927] [6, 12928] [6, 12930] [6, 12955] [6, 12956] [6, 12957] [6, 12970] [6, 12976] [6, 13010] [6, 13011] [6, 13028] [6, 13029] [6, 13030] [6, 13031] [6, 13038] [6, 13039] [6, 13040] [6, 13041] [6, 13042] [6, 13048] [6, 13049] [6, 13062] [6, 13063] [6, 13064] [6, 13325] [6, 13328] [6, 13329] [6, 13331] [6, 13405] [6, 13406] [6, 13415] [6, 13436] [6, 13437] [6, 13921] [6, 13938] [6, 13944] [6, 14114] [6, 14115] [6, 14238]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- x²y² ≈ xyx
- xyzx ≈ xyzx²
- xyzx ≈ xyzxz
- x²yzy²z ≈ xyzx
- xyx²yzy ≈ xyzx
- xyx²yz² ≈ xyzx
- xyxyxzx ≈ xyzx
- xyxyxzy ≈ xyzx
- xyxy²xz ≈ xyxz
- xyxy²zx ≈ xyzx
- xyxyzyx ≈ xyzx
- xyxzyxz ≈ xyzx
- xyxz²xy ≈ xyzx
- xyxz²yx ≈ xyzx
- xy²xz²x ≈ xyzx
- xyzx ≈ xyzxyzx
- xyzx ≈ xyzy²xz
- xyzx ≈ xyzy²zx
- xyzx ≈ xyzyzxy
- xyzx ≈ xyzyzyx
- xyzx ≈ xyzyz²x
- xyzy ≈ xyzyz²y