In this paper, we propose a novel verifier integration design focusing on the automatic theorem proving (ATP) task to solve the high computational cost and time consumption of reinforcement learning (RL)-based methods for artificial intelligence inference. Unlike existing methods that utilize feedback for the entire inference process, the proposed method uses an automatic verifier to provide intermediate feedback at each step of the inference process. Using Lean as a verifier, we experimentally show that step-by-step local verification improves the overall inference accuracy and efficiency of the model.