A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 42 semigroups of order six, all of which generate the variety V[6196]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-3c24dcac93cfa721 in the data of the bases-min seal.
Certified for
[6, 6196] [6, 6241] [6, 6482] [6, 6508] [6, 6513] [6, 6545] [6, 6599] [6, 6608] [6, 6841] [6, 6845] [6, 6874] [6, 6984] [6, 6988] [6, 7017] [6, 8908] [6, 9049] [6, 9842] [6, 9887] [6, 9925] [6, 10814] [6, 10818] [6, 10824] [6, 11148] [6, 11149] [6, 11153] [6, 11297] [6, 11303] [6, 11304] [6, 11308] [6, 11408] [6, 11413] [6, 11414] [6, 11415] [6, 11451] [6, 11455] [6, 11547] [6, 11548] [6, 11686] [6, 11700] [6, 11730] [6, 11777] [6, 11781]
The identities
- x² ≈ x⁴
- x²y ≈ xyx
- xy ≈ xy³
- xyz ≈ xzy