Unlikely Intersection Conjecture for semiabelian varieties

Let $G$ be a semiabelian variety defined over $\overline{\mathbb{Q}}$ and let $X\subseteq G$ be an algebraic subvariety. For an algebraic subgroup $H\subseteq G$, write $G^{[\dim(X)+1]}$ for the union of all such subgroups with $\operatorname{codim}_G(H)\geq \dim(X)+1$. Unlikely Intersection Conjecture. If $X$ is not contained in a proper algebraic subgroup of $G$, then $X\cap G^{[\dim(X)+1]}$ is not Zariski-dense in $X$. This is an unlikely-intersection statement for semiabelian varieties, predicted by conjectures of Pink and Zilber; its resolution status is not specified in the source.