A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 80 semigroups of order six, all of which generate the variety V[7398]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-faecb42565594d8b in the data of the bases-min seal.
Certified for
[6, 7398] [6, 7400] [6, 7436] [6, 7437] [6, 7485] [6, 7501] [6, 7798] [6, 7824] [6, 7836] [6, 7852] [6, 7952] [6, 7983] [6, 7997] [6, 8028] [6, 8040] [6, 8057] [6, 8128] [6, 8137] [6, 8149] [6, 8152] [6, 8153] [6, 10517] [6, 10535] [6, 10557] [6, 10559] [6, 10854] [6, 10921] [6, 11018] [6, 11027] [6, 11038] [6, 11043] [6, 11073] [6, 11081] [6, 11084] [6, 11282] [6, 11288] [6, 12564] [6, 12580] [6, 12628] [6, 12643] [6, 12689] [6, 12692] [6, 12708] [6, 12747] [6, 12765] [6, 12782] [6, 12843] [6, 12907] [6, 12909] [6, 12912] [6, 12913] [6, 12914] [6, 12916] [6, 12933] [6, 12935] [6, 12937] [6, 12961] [6, 12962] [6, 12963] [6, 12983] [6, 13015] [6, 13016] [6, 13032] [6, 13033] [6, 13052] [6, 13053] [6, 13337] [6, 13346] [6, 13349] [6, 13350] [6, 13352] [6, 13410] [6, 13417] [6, 13418] [6, 13423] [6, 13924] [6, 13940] [6, 14119] [6, 14120] [6, 14240]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyx ≈ xyxy
- xyxzx ≈ xyzx