An infinite family of sharply two-arc transitive digraphs

We disclaim Conjecture 1 posed by Seifter in N. Seifter, Transitive digraphs with more than one end, Discrete Math., to appear], that stated that a connected locally finite digraph with more than one end is either 0-, 1- or highly arc transitive. We describe in this work an infinite family of 2-arc transitive two-ended digraphs, that are not 3-arc transitive.