Existing approaches construct appropriate interaction models to explore semantic conflicts between claims and relevant articles, which provides practical solutions for interpretable claim verification. However, these conflicts are not necessarily all about questioning the false part of claims, which makes considerable semantic conflicts difficult to be used as evidence to explain the results of claim verification. In this paper, we propose evidence inference networks (EVIN), which focus on the conflicts questioning the core semantics of claims and serve as evidence for interpretable claim verification. Specifically, EVIN first captures the core semantic segments of claims and the users' principal opinions in relevant articles. Then, it finely-grained identifies the semantic conflicts contained in each relevant article from these opinions. Finally, it constructs coherence modeling to match the conflicts that queries the core semantic fragments of claims as explainable evidence. Experiments on two widely used datasets demonstrate that EVIN not only achieves satisfactory performance but also provides explainable evidence for end-users.