Renamable paramodulation for automatic theorem proving with equality

✍ Scribed by C.L. Chang

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 825 KB
• Volume: 1
• Category: Article
• ISSN: 0004-3702
• DOI: 10.1016/0004-3702(70)90010-x

✦ Synopsis

Roughly speaking, in automatic theorem proving with equality, paramodulation is a substitution rule for equality. In this paper, renamable resolution is extended to paramodulation. Renamable paramodulation is paramodulation of two clauses which become positive after an R-renaming. We prove.the R-refutation completeness of renamable resolution and renamable paramodulation for functionally reflexive systems. That is, we prove that, if a set S of clauses is R-unsatisfiable and if F is the set of the functionally reflexive axioms for S, then the empty clause can be derived from S & {x --x} & F by ttsing renamable resolution plus renamable paramodulation.