For simplicity, let's fervently hope that the initial explanation from one of the men was true...
Notice that Dante asks the second one if he is a truth-teller. There are only two possibilities, which are as follows:
1) Suppose the first one is a truth-teller and the second one is a liar. Since the first one always tells truth, it must be true that the second one would indeed say "yes" to Dante's question. Since the second one is a liar, this is indeed the case -- he would in fact say yes, despite the fact that the true answer is no. We find no contradiction here.
2) Now suppose the first one is a liar and the second one is a truth-teller. This means that the first one's assertion that the second one would say "yes" is a lie -- in other words, the second one would actually say "no." This, however, leads to a contradiction. If the second one is a truth-teller, his answer should be yes. Hence we rule out the possibility that the first one lies and the second one tells truth.
Answer: Trust the first one.
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