Pink–Mordell–Lang conjecture for semi-abelian varieties

Let $G$ be a semi-abelian variety over $\mathbb{C}$, let $\Gamma\subset G(\mathbb{C})$ be a subgroup of finite $\mathbb{Z}$-rank, and let $Z$ be an irreducible closed subvariety of dimension $d$. Define $G^{[>d]}$ as the union of algebraic subgroups of $G$ of codimension greater than $d$.

Pink–Mordell–Lang conjecture. If $Z$ is not contained in any translation of a proper algebraic subgroup of $G$, then $Z\cap(\Gamma+G^{[>d]})$ is not Zariski dense in $Z$.

The source states that this formulation is equivalent to the preceding semi-abelian Zilber–Pink conjecture, citing Pink's results. Its status is not otherwise specified.