Resolve the unsolved order-five implication

Determine whether the order-five implication with hypothesis $H:x=(y((z x) z))(y x)$ and target $T:x=(y z)((x(w z)) x)$ holds for all magmas, or construct a countermodel, including determining whether a five-element or infinite countermodel is necessary.

Background

The solver failed to produce an accepted certificate for one main-evaluation instance. The authors show that a right-projection intermediate law used by one proof route is impossible to derive from the hypothesis, but explicitly emphasize that this does not settle the original implication. Finite searches found no countermodel on carriers of sizes two or three and bounded searches found none on sizes four through six; the authors leave unresolved whether a five-element countermodel exists, whether an infinite countermodel is required, or whether the implication is universally valid.