A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 239 semigroups of order six, all of which generate the variety V[3178]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-b3ae7f8f532cfbfb in the data of the bases-min seal.
Certified for
[6, 3178] [6, 3180] [6, 3242] [6, 3961] [6, 4000] [6, 5892] [6, 5897] [6, 6011] [6, 6026] [6, 6046] [6, 6622] [6, 6648] [6, 6711] [6, 7059] [6, 7061] [6, 7086] [6, 7087] [6, 7104] [6, 7106] [6, 7113] [6, 7123] [6, 7128] [6, 7133] [6, 7284] [6, 7285] [6, 7286] [6, 7287] [6, 8569] [6, 8571] [6, 8596] [6, 8597] [6, 8696] [6, 8711] [6, 8712] [6, 8714] [6, 8760] [6, 8779] [6, 8781] [6, 8783] [6, 8784] [6, 8789] [6, 8792] [6, 9814] [6, 9822] [6, 9982] [6, 9984] [6, 9999] [6, 10000] [6, 10004] [6, 10019] [6, 10023] [6, 10028] [6, 10056] [6, 10060] [6, 10064] [6, 10076] [6, 10077] [6, 10136] [6, 10160] [6, 10428] [6, 10435] [6, 10438] [6, 10439] [6, 10440] [6, 10447] [6, 10490] [6, 10651] [6, 10654] [6, 10656] [6, 10664] [6, 10669] [6, 10670] [6, 10673] [6, 11606] [6, 11609] [6, 11643] [6, 11649] [6, 11659] [6, 11709] [6, 11724] [6, 11725] [6, 11727] [6, 11750] [6, 11826] [6, 11838] [6, 11847] [6, 11939] [6, 11941] [6, 11949] [6, 11950] [6, 11956] [6, 11958] [6, 11961] [6, 11967] [6, 11970] [6, 11973] [6, 12013] [6, 12014] [6, 12015] [6, 12016] [6, 12019] [6, 12024] [6, 12029] [6, 12031] [6, 12037] [6, 12075] [6, 12077] [6, 12080] [6, 12083] [6, 12087] [6, 12092] [6, 12110] [6, 12129] [6, 12131] [6, 12134] [6, 12135] [6, 12136] [6, 12150] [6, 12155] [6, 12165] [6, 12166] [6, 12202] [6, 12205] [6, 12208] [6, 12209] [6, 12218] [6, 12220] [6, 12221] [6, 12232] [6, 12235] [6, 12238] [6, 12251] [6, 12495] [6, 12496] [6, 12497] [6, 12498] [6, 12502] [6, 12503] [6, 12504] [6, 12505] [6, 12507] [6, 12509] [6, 12512] [6, 12513] [6, 12514] [6, 12515] [6, 12518] [6, 13808] [6, 13810] [6, 13818] [6, 13819] [6, 13825] [6, 13827] [6, 13830] [6, 13836] [6, 13839] [6, 13842] [6, 13882] [6, 13883] [6, 13884] [6, 13885] [6, 13888] [6, 14014] [6, 14021] [6, 14022] [6, 14025] [6, 14028] [6, 14031] [6, 14034] [6, 14035] [6, 14042] [6, 14082] [6, 14083] [6, 14084] [6, 14086] [6, 14087] [6, 14088] [6, 14091] [6, 14092] [6, 14187] [6, 14194] [6, 14224] [6, 14229] [6, 14279] [6, 14281] [6, 14283] [6, 14284] [6, 14287] [6, 14290] [6, 14325] [6, 14326] [6, 14327] [6, 14328] [6, 14331] [6, 14332] [6, 14334] [6, 14336] [6, 14337] [6, 14382] [6, 14385] [6, 14406] [6, 14408] [6, 14413] [6, 14414] [6, 14418] [6, 14453] [6, 14455] [6, 14476] [6, 14478] [6, 14480] [6, 14481] [6, 14483] [6, 14485] [6, 14486] [6, 14490] [6, 14492] [6, 14494] [6, 14502] [6, 14503] [6, 14504] [6, 14505] [6, 14508] [6, 14516] [6, 14520] [6, 14525] [6, 14527] [6, 14530] [6, 14532] [6, 14534] [6, 14535] [6, 14540] [6, 14545] [6, 14547] [6, 14548] [6, 14559] [6, 14561] [6, 14570] [6, 14574] [6, 14578]
The identities
- x² ≈ x³
- x²y ≈ xy
- xy ≈ xyx
- xyz ≈ xzy