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Conference Paper

Elimination of Equality via Transformation with Ordering Constraints

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44055

Bachmair,  Leo
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44474

Ganzinger,  Harald
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45678

Voronkov,  Andrei
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Bachmair, L., Ganzinger, H., & Voronkov, A. (1998). Elimination of Equality via Transformation with Ordering Constraints. In C. Kirchner, & H. Kirchner (Eds.), Proceedings of the 15th International Conference on Automated Deduction (CADE-98) (pp. 175-190). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-382F-0
Abstract
We refine Brand's method for eliminating equality axioms by (i) imposing ordering constraints on auxiliary variables introduced during the transformation process and (ii) avoiding certain transformations of positive equations with a variable on the right-hand side. The refinements are both of theoretical and practical interest. For instance, the second refinement is implemented in Setheo and appears to be critical for that prover's performance on equational problems. The correctness of this variant of Brand's method was an open problem that is solved by the more general results in the present paper. The experimental results we obtained from a prototype implementation of our proposed method for the model elimination prover Protein also show some dramatic improvements of the proof search. Ordering constraints have already been widely used in equational theorem provers based on paramodulation. We prove the correctness of our refinements of Brand's method by establishing a suitable connection to basic paramodulation calculi and thereby shed new light on the connection between different approaches to equational theorem proving.