Costa–Morini–Pasotti–Pellegrini simple-orderability conjecture

Let $G$ be an abelian group and let $X\subseteq G\setminus\{0\}$. Call $X$ simply orderable when its elements can be arranged so that every nonempty proper consecutive subsequence has nonzero sum. Costa–Morini–Pasotti–Pellegrini conjecture. If $X$ is finite and has zero sum, and there is no element $x$ such that $\{x,-x\}\subseteq X$, then $X$ is simply orderable. This is a conjecture about simple orderings in abelian groups, related to the notion of sequenceable groups; the source does not state that it has been resolved.