Large language models (LLMs) are increasingly used in high-stakes domains, yet their unfaithful or non-factual outputs create serious risks and hinder trustworthy deployment. Rigorous fact-checking is therefore essential to mitigate these risks. Most existing factuality verification methods improve evidence acquisition, but fail to capture complex logical relations between claims and multi-source evidence, especially when different evidence sources are inconsistent or incomplete. Moreover, current benchmarks rarely capture such realistic conflict scenarios. To address this, we introduce MAVEN, a real-world benchmark for verifying complex claims against heterogeneous and conflicting web evidence with fine-grained explanations. We further propose ArgCheck, an argumentation-based fact-checking framework. It models claims and retrieved evidence as arguments linked by attack relations, resolving conflicts through formal argumentation semantics. To avoid incomplete evidence, ArgCheck incorporates adversarial web retrieval to gather balanced multi-source evidence and grounds its verdicts and explanations in accepted arguments. Experiments on MAVEN and the public fact-checking benchmark AVeriTeC show that ArgCheck improves Macro-F1 over the strongest baseline by 5.39 and 11.10 points, respectively, while generating more faithful and evidence-grounded explanations. Our code and dataset are available online https://github.com/ZyraChen/ArgCheck.

Text-Attributed Graphs (TAGs), which are characterized with text attributes, are widely used in the real world. When evaluating fully trained models designed for TAG predictions, they may perform significantly unsatisfactory on samples outside the In-Distribution (ID) data, which may raise serious security issues. To tackle it, Out-Of-Distribution (OOD) detection is introduced to the TAGs field, which aims to utilize a detector to classify OOD and ID samples. Recent studies attempt to introduce extra OOD datasets to regularize the detection model. However, due to the vastness of the OOD data space, high-quality OOD samples for training the detector are scarce and difficult to obtain in the real world. Thus, we utilize Large Language Models (LLMs) to generate the OOD training samples with high quality. There are two issues in this process: (1) LLMs tend to generate OOD-node samples significantly different from ID ones, with a limited learning value for OOD and ID relations. (2) Due to the inherent structure of TAGs, obtained OOD nodes need to be integrated with existing nodes by generating edges using LLMs. However, the large number of nodes makes reasoning over each node pair computationally unbearable. Toward these issues, we introduce LLMGuard with challenging OOD-node generation and lightweight edge predictors. Extensive experiments prove the effectiveness of LLMGuard. The source code is available.