Redundancy checking (RC) is a key knowledge reduction technology. Extension rule (ER) is a new reasoning method, first presented in 2003 and well received by experts at home and abroad. Novel extension rule (NER) is an improved ER-based reasoning method, presented in 2009. In this paper, we first analyse the characteristics of the extension rule, and then present a simple algorithm for redundancy checking based on extension rule (RCER). In addition, we introduce MIMF, a type of heuristic strategy. Using the aforementioned rule and strategy, we design and implement RCHER algorithm, which relies on MIMF. Next we design and implement an RCNER (redundancy checking based on NER) algorithm based on NER. Parallel computing greatly accelerates the NER algorithm, which has weak dependence among tasks when executed. Considering this, we present PNER (parallel NER) and apply it to redundancy checking and necessity checking. Furthermore, we design and implement the RCPNER (redundancy checking based on PNER) and NCPPNER (necessary clause partition based on PNER) algorithms as well. The experimental results show that MIMF significantly influences the acceleration of algorithm RCER in formulae on a large scale and high redundancy. Comparing PNER with NER and RCPNER with RCNER, the average speedup can reach up to the number of task decompositions when executed. Comparing NCPNER with the RCNER-based algorithm on separating redundant formulae, speedup increases steadily as the scale of the formulae is incrementing. Finally, we describe the challenges that the extension rule will be faced with and suggest possible solutions.