A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 103 semigroups of order six, all of which generate the variety V[15024]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-b84c62af7408ba01 in the data of the bases-min seal.
Certified for
[6, 15024] [6, 15060] [6, 15080] [6, 15090] [6, 15098] [6, 15124] [6, 15131] [6, 15142] [6, 15150] [6, 15154] [6, 15156] [6, 15161] [6, 15162] [6, 15163] [6, 15168] [6, 15195] [6, 15239] [6, 15247] [6, 15304] [6, 15305] [6, 15310] [6, 15314] [6, 15326] [6, 15331] [6, 15344] [6, 15350] [6, 15353] [6, 15355] [6, 15357] [6, 15359] [6, 15361] [6, 15362] [6, 15363] [6, 15364] [6, 15367] [6, 15379] [6, 15402] [6, 15404] [6, 15414] [6, 15418] [6, 15438] [6, 15447] [6, 15452] [6, 15458] [6, 15464] [6, 15467] [6, 15470] [6, 15478] [6, 15500] [6, 15524] [6, 15543] [6, 15548] [6, 15552] [6, 15559] [6, 15566] [6, 15569] [6, 15575] [6, 15576] [6, 15577] [6, 15586] [6, 15599] [6, 15605] [6, 15608] [6, 15612] [6, 15615] [6, 15617] [6, 15623] [6, 15627] [6, 15636] [6, 15641] [6, 15643] [6, 15650] [6, 15654] [6, 15656] [6, 15683] [6, 15714] [6, 15732] [6, 15740] [6, 15747] [6, 15772] [6, 15779] [6, 15783] [6, 15787] [6, 15788] [6, 15795] [6, 15804] [6, 15810] [6, 15813] [6, 15817] [6, 15818] [6, 15824] [6, 15828] [6, 15832] [6, 15835] [6, 15837] [6, 15840] [6, 15841] [6, 15842] [6, 15843] [6, 15845] [6, 15850] [6, 15851] [6, 15852]
The identities
- x ≈ x²
- xyxz ≈ xyz