Captain inclusion conjecture for the tournament equilibrium set

Let $T$ be a tournament. A captain vertex is a vertex with the captain property used in the paper, and let $A$ be the set of all captain vertices of $T$. Captain inclusion conjecture. Then

$$A\subseteq \operatorname{TEQ}(T).$$

The motivation is that a captain vertex together with any of its slaves dominates all other vertices, while a dominating singleton is the unique minimal TEQ-retentive set. It remains open whether every captain vertex belongs to the tournament equilibrium set.