A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 111 semigroups of order six, all of which generate the variety V[4332]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-9a48abd4c0e98274 in the data of the bases-min seal.
Certified for
[6, 4332] [6, 9970] [6, 9976] [6, 11867] [6, 11875] [6, 11877] [6, 11888] [6, 11892] [6, 11895] [6, 11896] [6, 11901] [6, 11905] [6, 11910] [6, 11913] [6, 11923] [6, 14616] [6, 14625] [6, 14633] [6, 14638] [6, 14642] [6, 14647] [6, 14649] [6, 14650] [6, 14652] [6, 14663] [6, 14668] [6, 14672] [6, 14676] [6, 14678] [6, 14682] [6, 14685] [6, 14688] [6, 14696] [6, 14700] [6, 14702] [6, 14705] [6, 14706] [6, 14708] [6, 14710] [6, 14711] [6, 14712] [6, 14713] [6, 14715] [6, 14717] [6, 14722] [6, 14723] [6, 14724] [6, 14726] [6, 14731] [6, 14733] [6, 14734] [6, 14735] [6, 14742] [6, 14747] [6, 14751] [6, 14756] [6, 14758] [6, 14759] [6, 14760] [6, 14761] [6, 14763] [6, 14764] [6, 14770] [6, 14773] [6, 14775] [6, 14777] [6, 14779] [6, 14781] [6, 14782] [6, 14784] [6, 14786] [6, 14791] [6, 14804] [6, 14805] [6, 14807] [6, 14809] [6, 14812] [6, 14821] [6, 14823] [6, 14824] [6, 14825] [6, 14826] [6, 14829] [6, 14831] [6, 14834] [6, 14835] [6, 14836] [6, 14839] [6, 14841] [6, 14843] [6, 14845] [6, 14847] [6, 14850] [6, 14860] [6, 14862] [6, 14863] [6, 14864] [6, 14865] [6, 14868] [6, 14869] [6, 14870] [6, 14871] [6, 14873] [6, 14875] [6, 14877] [6, 14878] [6, 14879] [6, 14881] [6, 14882] [6, 14884] [6, 14886]
The identities
- x ≈ x³
- x²y ≈ xyx