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Though chatbots based on large neural models can often produce fluent responses in open domain conversations, one salient error type is contradiction or inconsistency with the preceding conversation turns. Previous work has treated contradiction detection in bot responses as a task similar to natural language inference, e.g., detect the contradiction between a pair of bot utterances. However, utterances in conversations may contain co-references or ellipsis, and using these utterances as is may not always be sufficient for identifying contradictions. This work aims to improve the contradiction detection via rewriting all bot utterances to restore antecedents and ellipsis. We curated a new dataset for utterance rewriting and built a rewriting model on it. We empirically demonstrate that this model can produce satisfactory rewrites to make bot utterances more complete. Furthermore, using rewritten utterances improves contradiction detection performance significantly, e.g., the AUPR and joint accuracy scores (detecting contradiction along with evidence) increase by 6.5% and 4.5% (absolute increase), respectively.