A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 180 semigroups of order six, all of which generate the variety V[15001]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-5eb3ebb90f1b5788 in the data of the bases-min seal.
Certified for
[6, 15001] [6, 15003] [6, 15005] [6, 15006] [6, 15008] [6, 15010] [6, 15011] [6, 15015] [6, 15017] [6, 15019] [6, 15027] [6, 15028] [6, 15029] [6, 15030] [6, 15033] [6, 15035] [6, 15038] [6, 15039] [6, 15042] [6, 15049] [6, 15051] [6, 15052] [6, 15054] [6, 15058] [6, 15059] [6, 15067] [6, 15068] [6, 15070] [6, 15071] [6, 15072] [6, 15073] [6, 15083] [6, 15084] [6, 15085] [6, 15086] [6, 15103] [6, 15105] [6, 15107] [6, 15108] [6, 15110] [6, 15112] [6, 15113] [6, 15117] [6, 15119] [6, 15121] [6, 15126] [6, 15172] [6, 15173] [6, 15174] [6, 15175] [6, 15177] [6, 15179] [6, 15182] [6, 15183] [6, 15184] [6, 15185] [6, 15188] [6, 15198] [6, 15200] [6, 15203] [6, 15206] [6, 15211] [6, 15216] [6, 15218] [6, 15219] [6, 15222] [6, 15223] [6, 15224] [6, 15226] [6, 15228] [6, 15232] [6, 15236] [6, 15254] [6, 15255] [6, 15256] [6, 15258] [6, 15259] [6, 15260] [6, 15264] [6, 15265] [6, 15268] [6, 15270] [6, 15272] [6, 15275] [6, 15278] [6, 15282] [6, 15318] [6, 15319] [6, 15320] [6, 15334] [6, 15341] [6, 15342] [6, 15372] [6, 15373] [6, 15374] [6, 15382] [6, 15385] [6, 15387] [6, 15391] [6, 15394] [6, 15395] [6, 15396] [6, 15398] [6, 15419] [6, 15423] [6, 15424] [6, 15425] [6, 15426] [6, 15455] [6, 15456] [6, 15457] [6, 15483] [6, 15485] [6, 15487] [6, 15488] [6, 15490] [6, 15491] [6, 15492] [6, 15493] [6, 15503] [6, 15505] [6, 15506] [6, 15507] [6, 15508] [6, 15509] [6, 15514] [6, 15516] [6, 15519] [6, 15520] [6, 15521] [6, 15523] [6, 15530] [6, 15531] [6, 15533] [6, 15534] [6, 15538] [6, 15580] [6, 15581] [6, 15582] [6, 15660] [6, 15662] [6, 15664] [6, 15665] [6, 15667] [6, 15669] [6, 15670] [6, 15674] [6, 15676] [6, 15678] [6, 15686] [6, 15687] [6, 15688] [6, 15691] [6, 15693] [6, 15696] [6, 15697] [6, 15700] [6, 15708] [6, 15712] [6, 15713] [6, 15719] [6, 15720] [6, 15722] [6, 15723] [6, 15724] [6, 15725] [6, 15735] [6, 15736] [6, 15751] [6, 15753] [6, 15755] [6, 15756] [6, 15758] [6, 15760] [6, 15761] [6, 15765] [6, 15767] [6, 15769] [6, 15774] [6, 15790]
The identities
- x ≈ x²
- xyz ≈ xzy