Fact-checking claims is a highly laborious task that involves understanding how each factual assertion within the claim relates to a set of trusted source materials. Existing approaches make sample-level predictions but fail to identify the specific aspects of the claim that are troublesome and the specific evidence relied upon. In this paper, we introduce a method and new benchmark for this challenging task. Our method predicts the fine-grained logical relationship of each aspect of the claim from a set of multimodal documents, which include text, image(s), video(s), and audio(s). We also introduce a new benchmark (M3DC) of claims requiring multimodal multidocument reasoning, which we construct using a novel claim synthesis technique. Experiments show that our approach outperforms other models on this challenging task on two benchmarks while providing finer-grained predictions, explanations, and evidence.