Infinite Gallai–Milgram conjecture

Let $D$ be a digraph without infinite directed paths. Infinite Gallai–Milgram conjecture. There is a vertex-partition $d4ab$ of $D$ into directed paths and an independent set $U$ of vertices such that $U$ meets every $P":[?]$ This conjecture extends the finite Gallai–Milgram theorem to digraphs without infinite directed paths. Its restriction to acyclic digraphs follows from the infinite version of König's theorem, but the general conjecture remains unresolved according to the source.