Laborde–Payan–Xuong conjecture on independent sets meeting longest paths

Let $D$ be a digraph, and call a set of vertices independent if no two of its vertices are joined by an arc. A path in $D$ is longest if it has maximum length among all paths in $D$. Laborde–Payan–Xuong conjecture. Every digraph has an independent set meeting every longest path. The conjecture is presented as an open problem from 1983; the paper does not state a resolution in the supplied text.