Frey's ABC conjecture for number fields

Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and discriminant $\Delta_K$. For $\epsilon>0$ and a non-zero integral ideal $\mathfrak{a}$ of $\mathcal{O}_K$, let $c(\epsilon,\log|\Delta_K|,\log N_K(\mathfrak{a}))$ be a constant. Suppose that $A,B\in\mathcal{O}_K\setminus\{0\}$ generate the ideal $\mathfrak{a}$. Frey's ABC conjecture. There exists such a constant such that

$$\max\{h_K(A),h_K(B),h_K(A-B)\}\leq(1+\epsilon)\log\left(\prod_{\mathfrak{p}\mid AB(A-B)}N_K(\mathfrak{p})\right)+c(\epsilon,\log|\Delta_K|,\log N_K(\mathfrak{a})).$$

This is a refined ABC conjecture for number fields proposed by Frey. The source gives no evidence of a resolution, so it remains open.