Hochstättler's even-subgraph contraction conjecture for 3-edge-connected digraphs

Let $D=(V,A)$ be a 3-edge-connected digraph. An even subgraph $E\subseteq A$ is an edge-disjoint union of cycles of $D$, where the cycles need not be directed, and $D/E$ is the graph obtained by contracting the edges of $E$. Hochstättler's conjecture. There exists an even subgraph $E\subseteq A$ such that $D/E$ is strongly connected. The conjecture is false: the method developed in the paper produces a counterexample.