I've encountered the negative contraction several times since I started to study japanese, and I understand the logic behind the transformation from 開かない/開かぬ to 開かん in the first picture.
A similar transformation seems to occur in the following two sentences, とならん and ならん. However, when I check the translation the form of the verbs are positive.
There is something I'm missing and I can't find the key to know the difference between this similar sounding contractions.