The solution of an open problem on semigroup inclusion classes

The semigroup inclusion class $$\mathbf{I}$ = [xyxy = xy; xyz \in {xywz, xuyz}]$istheunionoftwomaximalsubvarietiesof$$\mathbf{G}\mathbf{R}\mathbf{B}$ = [xyzxy=xy]$. Monzo ( arXiv:1411.4860 ) described the lattice of semigroup inclusion classes below $\mathbf{I}$ and asked if $\mathbf{I}$ is covered by $\mathbf{G}\mathbf{R}\mathbf{B}$. Our main result is a characterization of $\mathbf{I}$ which makes it easy to answer Monzo’s question in the negative.