A Novel Theorem Proving Algorithm Based on Extension Rule

ATP (automated theorem proving) has always been one of the most advanced areas of computer science. The traditional idea used in ATP is to try to deduce the empty clause to check satisfiability, such as resolution based theorem proving, which is one of the most popular methods. Extension-rule-based theorem proving is a new resolution-based theorem proving method. After a deep research work on the extension rule, a brilliant property of the rule is obtained. In this paper, the property and an algorithm which is used to decide it are proposed firstly. In addition, the algorithms time complexity and space complexity are analyzed and proved. Based on the above work, a novel extension rule based theorem proving algorithm called NER is proposed. The NER algorithm transforms the problem which decides whether a clause set is satisfiable to a series of problems deciding whether one literal set includes another one, while the original extension algorithm transforms them to problems counting the number of maximum terms that can be expended. A number of experiments show that the NER algorithm obviously outperforms both the original extension rule based algorithm ER and the directional resolution algorithm DR. Especially, it can be improved up to two orders of magnitude.