Fraenkel's conjecture on the moduli of disjoint covering systems

Let $\{S(\alpha_i,\beta_i)\}_{i=1}^n$ be a disjoint covering system (DCS) of rational Beatty sequences, with $n>2$, and suppose that

$$\alpha_1<\alpha_2<\cdots<\alpha_n.$$

Fraenkel's conjecture. If the system has no multiplicity, then $\alpha_i=p/q_i$, where

$$\np=2^n-1,\qquad q_i=2^{n-i},\qquad i=1,2,\ldots,n.$$

This is the precise formulation given after the general classification claim: it identifies the moduli of the conjecturally unique family, up to the translation freedom in the Beatty sequences. Its resolution is not established by the supplied text.