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SPASS-AR: A First-Order Theorem Prover Based on Approximation-Refinement into the Monadic Shallow Linear Fragment

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Abstract

We introduce FO-AR, an approximation-refinement approach for first-order theorem proving based on counterexample-guided abstraction refinement. A given first-order clause set N is transformed into an over-approximation \(N^{\prime }\) in a decidable first-order fragment. That means if \(N^{\prime }\) is satisfiable so is N. However, if \(N^{\prime }\) is unsatisfiable, then the approximation provides a lifting terminology for the found refutation which is step-wise transformed into a proof of unsatisfiability for N. If this fails, the cause is analyzed to refine the original clause set such that the found refutation is ruled out for the future and the procedure repeats. The target fragment of the transformation is the monadic shallow linear fragment with straight dismatching constraints, which we prove to be decidable via ordered resolution with selection. We further discuss practical aspects of SPASS-AR, a first-order theorem prover implementing FO-AR. We focus in particularly on effective algorithms for lifting and refinement.

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Acknowledgements

We thank the reviewers as well as Konstantin Korovin and Giles Reger for a number of important remarks.

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  1. Max-Planck Institut für Informatik, Saarland Informatics Campus E1 4, 66123, Saarbrücken, Germany

    Andreas Teucke & Christoph Weidenbach

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  1. Andreas Teucke
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  2. Christoph Weidenbach
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Correspondence to Christoph Weidenbach.

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Teucke, A., Weidenbach, C. SPASS-AR: A First-Order Theorem Prover Based on Approximation-Refinement into the Monadic Shallow Linear Fragment. J Autom Reasoning 64, 611–640 (2020). https://doi.org/10.1007/s10817-020-09546-z

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