MSO$_2$-orderability conjecture for VR-equational classes with property SEP

Let $\mathcal{C}$ be a VR-equational class of graphs. Say that $\mathcal{C}$ has property $\mathsf{SEP}$ when it satisfies the separation property defined in the surrounding theory. The VR-equational MSO$_2$-orderability conjecture. Every VR-equational class that has property $\mathsf{SEP}$ is $\mathrm{MSO}_2$-orderable. The corresponding statement is established in the paper for HR-equational classes, but decidability is not obtained for VR-equational classes; the conjecture proposes that the same implication holds for all VR-equational classes.