A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 8 semigroups of order six, all of which generate the variety V[5324]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-1d3b7f5f8b01bf14 in the data of the bases-min seal.

Certified for

[6, 5324] [6, 5327] [6, 5328] [6, 5331] [6, 9335] [6, 9338] [6, 9400] [6, 9403]

The identities

xy ≈ yx
x⁵y ≈ xy
xy ≈ xy⁵
xy ≈ xyxyxyxyxy