Though prompting LLMs with various reasoning structures produces reasoning proofs along with answers, these proofs are not ensured to be causal and reliable due to the inherent defects of LLMs. Tracking such deficiencies, we present a neuro-symbolic integration method, in which a neural LLM is used to represent the knowledge of the problem while an LLM-free symbolic solver is adopted to do deliberative reasoning using the knowledge. Specifically, our customized meta-interpreters allow the production of reasoning proofs and support flexible search strategies. These reasoning proofs are ensured to be causal and reliable because of the deterministic executing nature of the symbolic solvers. Empirically, on ProofWriter, our method surpasses the CoT baseline by nearly double in accuracy and more than triple in proof similarity. On GSM8K, our method also shows accuracy improvements and nearly doubled proof similarity. Our code is released at https://github.com/DAMO-NLP-SG/CaRing

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