A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 119 semigroups of order six, all of which generate the variety V[962]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ff9cbff005222804 in the data of the bases-min seal.
Certified for
[6, 962] [6, 1208] [6, 2904] [6, 3056] [6, 3171] [6, 3179] [6, 3954] [6, 3999] [6, 4005] [6, 5766] [6, 5885] [6, 5895] [6, 5917] [6, 6612] [6, 6640] [6, 6707] [6, 6719] [6, 6725] [6, 6763] [6, 7055] [6, 7060] [6, 7088] [6, 7122] [6, 7127] [6, 8565] [6, 8570] [6, 8695] [6, 8697] [6, 8749] [6, 8778] [6, 8780] [6, 8787] [6, 8791] [6, 8793] [6, 8795] [6, 9807] [6, 9818] [6, 9979] [6, 9983] [6, 10002] [6, 10007] [6, 10047] [6, 10058] [6, 10063] [6, 10132] [6, 10159] [6, 10165] [6, 10167] [6, 11603] [6, 11607] [6, 11615] [6, 11708] [6, 11710] [6, 11740] [6, 11818] [6, 11824] [6, 11837] [6, 11839] [6, 11849] [6, 11937] [6, 11940] [6, 11951] [6, 11966] [6, 11969] [6, 12020] [6, 12028] [6, 12033] [6, 12035] [6, 12109] [6, 12201] [6, 12204] [6, 12216] [6, 12231] [6, 12234] [6, 13806] [6, 13809] [6, 13820] [6, 13835] [6, 13838] [6, 14013] [6, 14015] [6, 14030] [6, 14032] [6, 14040] [6, 14182] [6, 14192] [6, 14278] [6, 14280] [6, 14285] [6, 14289] [6, 14293] [6, 14295] [6, 14380] [6, 14384] [6, 14386] [6, 14390] [6, 14437] [6, 14439] [6, 14475] [6, 14477] [6, 14482] [6, 14489] [6, 14491] [6, 14514] [6, 14518] [6, 14529] [6, 14531] [6, 14539] [6, 14543] [6, 14552] [6, 14554] [6, 14568] [6, 14572] [6, 14576] [6, 14582] [6, 14584] [6, 14589] [6, 14596] [6, 14598]
The identities
- x² ≈ x³
- xy ≈ yx
- x²y ≈ xy