Extension rule-based theorem proving is a splendid reasoning method. Based on the extension rule algorithm IER (improved extension rule), this paper proposes IMOM (improved maximum occurrences on clauses of maximum size) and IBOHM (improved BOHM) heuristic strategies in order to give guidance while choosing the clause that limits the search space. This paper applies these two heuristic strategies to the algorithm IER, designs and implements the algorithms IMOMH_IER and IBOHMH_IER. Since more appropriate search space can be obtained with these two heuristic strategies, the algorithms can decide whether the original question is satisfiable in a fraction of a second. Experimental results show that the speed of the algorithms is 10~200 times that of the existing algorithms DR (directional resolution) and IER.