A complementary ratio based clause selection method for contradiction separation dynamic deduction

Automated reasoning is a key research area of Artificial Intelligence (AI) and has attracted much greater attention in recent years due to the demands of trustworthy AI, where binary resolution inference rule based first-order automated reasoning play a crucial role. Recently, a novel multi-clause dynamic standard contradiction separation (S-CS) inference rule and related automated deduction theory were proposed to overcome the limitations of binary resolution-based automated deduction. Now that strategies for dynamic clause selection are essential for S-CS based automated deduction, in the present work, a class of novel clause selection strategies, along with the corresponding novel complementary ratio based dynamic S-CS automated deduction algorithm (called CRA), are proposed. Furthermore, we are interested in determining whether CRA may be deployed on top of the current best first-order automated reasoning system designs to increase their performance. As a result, CRA is applied to the current leading systems, Vampire and E, resulting in two integrated automatic reasoning systems, CRA_Vampire and CRA_E. Experiment results demonstrate that CRA can improve E and Vampire in CASC 2020–2022 competitions. The new integrated automated reasoning systems can resolve 44 problems with rating of 1, meaning they are intractable by other existing first-order automated systems.