A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 9 semigroups of order six, all of which generate the variety V[2741]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-7ba081cdd598de0f in the data of the bases-min seal.

Certified for

[6, 2741] [6, 2742] [6, 2753] [6, 2754] [6, 2760] [6, 5211] [6, 5222] [6, 5247] [6, 9306]

The identities

x³ ≈ x⁴
xyx ≈ yx²
x²y² ≈ xy²x
x²yz ≈ xyxz