A certified basis of 3 identities

This list of identities is a basis, proved in Lean, of 345 semigroups of order six, all of which generate the variety V[977]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-abf66f21577c1897 in the data of the bases-min seal.

Certified for

[6, 977] [6, 979] [6, 981] [6, 983] [6, 985] [6, 987] [6, 1003] [6, 1004] [6, 1005] [6, 1013] [6, 1014] [6, 1016] [6, 1018] [6, 1019] [6, 1022] [6, 1023] [6, 1026] [6, 1027] [6, 1031] [6, 1034] [6, 1038] [6, 1050] [6, 1071] [6, 1072] [6, 1074] [6, 1079] [6, 1080] [6, 1081] [6, 1083] [6, 1084] [6, 1085] [6, 1086] [6, 1089] [6, 1093] [6, 1096] [6, 1104] [6, 1109] [6, 1126] [6, 1141] [6, 1142] [6, 1143] [6, 1144] [6, 1145] [6, 1146] [6, 1149] [6, 1151] [6, 1153] [6, 1155] [6, 1157] [6, 1161] [6, 1178] [6, 1202] [6, 2942] [6, 2946] [6, 2951] [6, 2972] [6, 2989] [6, 2993] [6, 2995] [6, 3004] [6, 3024] [6, 3026] [6, 3028] [6, 3038] [6, 3246] [6, 3248] [6, 3250] [6, 3253] [6, 3255] [6, 3257] [6, 3271] [6, 3273] [6, 3275] [6, 3277] [6, 3285] [6, 3287] [6, 3289] [6, 3295] [6, 3297] [6, 3326] [6, 3327] [6, 3328] [6, 3335] [6, 3337] [6, 3347] [6, 3349] [6, 3356] [6, 3382] [6, 3384] [6, 3397] [6, 3401] [6, 3403] [6, 3404] [6, 3406] [6, 3408] [6, 3409] [6, 3426] [6, 3427] [6, 3428] [6, 3429] [6, 3431] [6, 3433] [6, 3459] [6, 3463] [6, 3487] [6, 3490] [6, 3525] [6, 3540] [6, 3549] [6, 3563] [6, 3564] [6, 3565] [6, 3566] [6, 3568] [6, 3575] [6, 3577] [6, 3579] [6, 3586] [6, 3592] [6, 3602] [6, 3614] [6, 3629] [6, 3630] [6, 3631] [6, 3633] [6, 3634] [6, 3635] [6, 3666] [6, 3669] [6, 3725] [6, 3738] [6, 3851] [6, 3852] [6, 3882] [6, 3883] [6, 3884] [6, 3885] [6, 3887] [6, 3890] [6, 3892] [6, 3895] [6, 3900] [6, 3904] [6, 3910] [6, 3915] [6, 3920] [6, 3964] [6, 3966] [6, 3968] [6, 3974] [6, 3976] [6, 3978] [6, 3979] [6, 3983] [6, 3987] [6, 3988] [6, 3989] [6, 3992] [6, 5804] [6, 5810] [6, 5906] [6, 5908] [6, 5910] [6, 5916] [6, 5944] [6, 5946] [6, 5969] [6, 5971] [6, 5990] [6, 6051] [6, 6052] [6, 6055] [6, 6057] [6, 6060] [6, 6061] [6, 6065] [6, 6093] [6, 6095] [6, 6098] [6, 6099] [6, 6103] [6, 6182] [6, 6200] [6, 6201] [6, 6226] [6, 6228] [6, 6230] [6, 6248] [6, 6250] [6, 6251] [6, 6254] [6, 6271] [6, 6272] [6, 6275] [6, 6277] [6, 6280] [6, 6288] [6, 6290] [6, 6291] [6, 6293] [6, 6294] [6, 6295] [6, 6298] [6, 6355] [6, 6465] [6, 6495] [6, 6497] [6, 6554] [6, 6556] [6, 6557] [6, 6560] [6, 6565] [6, 6566] [6, 6569] [6, 6570] [6, 6572] [6, 6577] [6, 6591] [6, 6630] [6, 6634] [6, 6651] [6, 6653] [6, 6655] [6, 6666] [6, 6669] [6, 6670] [6, 6674] [6, 6684] [6, 6685] [6, 6686] [6, 6689] [6, 6697] [6, 6731] [6, 6732] [6, 6733] [6, 6742] [6, 6747] [6, 7293] [6, 7296] [6, 7304] [6, 7306] [6, 7321] [6, 7329] [6, 7331] [6, 7345] [6, 7351] [6, 7356] [6, 7359] [6, 7371] [6, 7373] [6, 7455] [6, 7461] [6, 7463] [6, 7550] [6, 7554] [6, 7559] [6, 7562] [6, 7566] [6, 7570] [6, 7596] [6, 7601] [6, 7606] [6, 7694] [6, 7697] [6, 7702] [6, 7722] [6, 7724] [6, 7733] [6, 7735] [6, 7751] [6, 7766] [6, 7772] [6, 7774] [6, 8298] [6, 8299] [6, 8303] [6, 8304] [6, 8307] [6, 8308] [6, 8512] [6, 8515] [6, 8520] [6, 8525] [6, 8527] [6, 8600] [6, 8603] [6, 8611] [6, 8613] [6, 8630] [6, 8634] [6, 8638] [6, 8640] [6, 8685] [6, 8686] [6, 8725] [6, 8727] [6, 8735] [6, 8737] [6, 8768] [6, 8773] [6, 9831] [6, 9865] [6, 9897] [6, 9940] [6, 10031] [6, 10034] [6, 10036] [6, 10038] [6, 10092] [6, 10095] [6, 10113] [6, 10115] [6, 10124] [6, 10129] [6, 10155] [6, 10256] [6, 10258] [6, 10287] [6, 10289] [6, 10303] [6, 10324] [6, 10327] [6, 10708] [6, 10710] [6, 10745] [6, 10751] [6, 10753] [6, 10754] [6, 10755] [6, 10797] [6, 11176] [6, 11181] [6, 11182] [6, 11464] [6, 11467] [6, 11484] [6, 11556] [6, 11560] [6, 11563] [6, 11583] [6, 11614] [6, 11631] [6, 11664] [6, 11702] [6, 11823]

The identities

x² ≈ x³
x²y² ≈ y²x²
xyz ≈ yxz