Non-separating cycle with a nowhere-zero 4-flow conjecture

Let $G$ be a cyclically $4$-edge connected cubic graph. For a cycle $C$ of $G$, let $G/E(C)$ denote the graph obtained by contracting the edges of $C$, and let a nowhere-zero $4$-flow mean a nowhere-zero flow over a group of order $4$. Non-separating cycle with a nowhere-zero $4$-flow conjecture. The graph $G$ contains a non-separating cycle $C$ such that $G/E(C)$ has a nowhere-zero $4$-flow. The source states that this conjecture would imply the cycle double cover conjecture and, in particular, the $5$-cycle double cover conjecture.