Puech's forbidden-subgraph conjecture for irredundance perfect graphs

Let $G$ be a graph, and let $P_6$, $G_4$, and $G_5$ be the graphs described in Figure 5 of the source. Puech's conjecture. If $G$ does not contain $P_6$, $G_4$, or $G_5$ as induced subgraphs, then $G$ is irredundance perfect. The supplied text introduces this as a generalization of the preceding conjectures but gives no resolution of it, so its status remains open.