CMPP conjecture on sequenceability of zero-sum subsets without inverse pairs

Let $G$ be an abelian group, and let $A$ be a finite subset of $G\setminus\{0\}$. An ordering $a_1,\ldots,a_{|A|}$ of $A$ is sequenceable if its partial sums

$$p_i=a_1+\cdots+a_i$$

are pairwise distinct and $p_i\ne 0$ for every $1\leq i\leq |A|-1$. CMPP conjecture. Every subset $A\subseteq G\setminus\{0\}$ whose elements sum to zero and such that $\{x,-x\}\not\subset A$ for every $x\in G$ is sequenceable. The conjecture concerns sequenceability in connection with Heffter arrays; the supplied text does not establish its general status, although it proves the claim for zero-sum subsets without inverse pairs of size at most $23$.