Terwilliger's finiteness conjecture for amply regular graphs

Let $G$ be an amply regular graph with parameters $(n,d,\alpha,\beta)$, where $n$ is possibly infinite. Terwilliger's conjecture. If $\beta\geq 2$, then $G$ is finite. Terwilliger's diameter bounds confirm this conjecture for amply regular graphs with $1\neq\beta\geq\alpha$; the general case remains open.