Wilf-equivalence conjecture for the 13 pattern sets in Corollary 3

Let the $13$ pattern sets be the sets referred to in Corollary~, and let $\{13452,23451\}$ be represented by the partially ordered pattern (POP) shown in the source. Wilf-equivalence conjecture. The $13$ pattern sets in Corollary~ are Wilf-equivalent to $\{13452,23451\}$.

The conjecture proposes a common Wilf-equivalence class for the listed pattern sets and the displayed POP. The source gives no resolution of this claim.