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The core difficulty lies in the complexity of entangled narratives and heterogeneous conflict patterns, which frequently exceeds the reasoning capacity of standard backbone architectures. We propose \\textbf{\\textsc{Kcr}} (Knowledge Conflict Reasoning), a framework that adjudicates contradictions by systematically structuring their underlying logic. \\textsc{Kcr} disentangles conflicting contexts into discrete sets of reasoning traces, utilizing a hybrid representation of text and graphs to facilitate systematic comprehension. 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