A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 121 semigroups of order six, all of which generate the variety V[3197]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-9cc2caa343353470 in the data of the bases-min seal.
Certified for
[6, 3197] [6, 3209] [6, 3217] [6, 3227] [6, 3234] [6, 3240] [6, 5948] [6, 5974] [6, 5994] [6, 6762] [6, 7071] [6, 7079] [6, 7084] [6, 7114] [6, 7116] [6, 7118] [6, 7144] [6, 7150] [6, 7153] [6, 7156] [6, 7159] [6, 7162] [6, 7173] [6, 7192] [6, 7199] [6, 7200] [6, 7205] [6, 7212] [6, 7236] [6, 7244] [6, 7246] [6, 7250] [6, 7256] [6, 7271] [6, 7274] [6, 7280] [6, 8581] [6, 8589] [6, 8594] [6, 9867] [6, 9991] [6, 9997] [6, 10049] [6, 10052] [6, 10074] [6, 10086] [6, 10089] [6, 10138] [6, 10142] [6, 10157] [6, 10158] [6, 10240] [6, 10264] [6, 10277] [6, 10282] [6, 10307] [6, 10312] [6, 10331] [6, 10332] [6, 10342] [6, 10344] [6, 10347] [6, 10349] [6, 10354] [6, 11633] [6, 11947] [6, 11962] [6, 11978] [6, 11981] [6, 12000] [6, 12003] [6, 12009] [6, 12044] [6, 12048] [6, 12067] [6, 12071] [6, 12097] [6, 12101] [6, 12114] [6, 12119] [6, 12128] [6, 12167] [6, 12171] [6, 12192] [6, 12215] [6, 12229] [6, 12243] [6, 12246] [6, 12267] [6, 12270] [6, 12272] [6, 12275] [6, 12281] [6, 12290] [6, 12297] [6, 12300] [6, 12311] [6, 12320] [6, 12406] [6, 12421] [6, 12424] [6, 12428] [6, 12432] [6, 12436] [6, 12443] [6, 12448] [6, 12451] [6, 12458] [6, 12483] [6, 13816] [6, 13831] [6, 13847] [6, 13850] [6, 13869] [6, 13872] [6, 13878] [6, 14071] [6, 14075] [6, 14216] [6, 14304] [6, 14320]
The identities
- x² ≈ x³
- x²y ≈ xy
- xyx ≈ yx²
- xyz ≈ yxz