Klee–Wolfe nonrevisiting path conjecture for polytopes

Let $P$ be a $d$-dimensional polytope, and let $u$ and $v$ be any two of its vertices. A path is nonrevisiting if, after leaving a facet, it does not later return to that facet. Nonrevisiting Path Conjecture. There is a path from $u$ to $v$ that does not revisit any facet it has left before. The conjecture would imply the Hirsch bound by giving paths of length at most $n-d$ when $P$ has $n$ facets. The supplied text attributes the conjecture to Klee and Wolfe and states that Santos's counterexamples to the Hirsch Conjecture also disprove it.