Short single fault detection tests of contact break for contact circuits with two or more additional poles

We consider the problem of synthesizing multi-pole contact circuits that implement given Boolean functions between poles $A$ and $B$ and allow short single fault detection tests related to contact breaks. For each Boolean function on $n$ variables and each test pole set containing at least two disjoint pairs of poles other than $\{A,B\}$, the minimal possible length value of such a test is found. In particular, it is proved that this value does not exceed $2$.