On recognizing integer polyhedra (Q2639642)

Given a rational system Ax\(\leq b\) of linear inequalities, does it determine an integer polyhedron? In \textit{A. Schrijver} [Discrete Appl. Math. 14, 111-133 (1986; Zbl 0602.90111)] noted that this problem is in co-NP. He asked whether this problem is also in NP. In this note, the authors proved that the problem is co-NP complete. So, it is unlikely in NP.