Extension rule reasoning method has been widely used in solving the classical satisfiability problem. Several reasoning methods based on extension rule have been proposed, which have been recognized around the world. These methods include the complete algorithms like NER, IMOMH_IER, PPSER, and local search-based incomplete algorithm like ERACC. All of them have sound performance. ERACC algorithm is the most efficient and powerful algorithm in the current extension rule solver. However, the serial algorithm ERACC still needs improvement on heuristics and preprocessing. Therefore, a parallel framework is designed and it is called PERACC algorithm. Based on the configuration checking of local search method, the algorithm decomposes the original maximum term space into several maximum term subspaces, from three stages of assigning initial values to variables, simplifying solution space, and heuristic, simplifying the original clause set, then processing each subspace in parallel. Experiments show that, compared with the original algorithm, the proposed algorithm not only can improve the efficiency of solution, but also can solve larger benchmark, which makes the extension rule method break through the limitation of formula size again.