Numerous studies have been conducted on automatic fact-checking, driven by its importance in real-world applications. However, two challenges persist: (1) extracting pivotal evidence from extensive documents, and (2) verifying claims across diverse domains. On one hand, current retrieval methods are limited in their ability to concisely retrieve evidence, which results in poor performance. On the other hand, retrieved evidence derived from different sources strains the generalization capabilities of classifiers. This paper explores the task of cross-domain fact-checking and presents the XClaimCheck dataset, which consists of claims from multiple domains. We propose a framework featuring a multi-argument generation technique. We leverage multi-argument generation to reconstruct concise evidence from large amounts of evidence retrieved from different sources. In addition, a self-refinement mechanism is introduced to confirm that the generated arguments are consistent with the content of the evidence. Experimental results show that our proposed framework is effective in identifying the veracity of out-of-domain claims, particularly those that are partially true or false.