Abstract
We present a formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving in Isabelle/HOL, culminating with a refutationally complete first-order prover based on ordered resolution with literal selection. We develop general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. Our work clarifies several of the fine points in the chapter’s text, emphasizing the value of formal proofs in the field of automated reasoning.
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Acknowledgment
Christoph Weidenbach discussed Bachmair and Ganzinger’s chapter with us on many occasions and hosted Schlichtkrull at the Max-Planck-Institut in Saarbrücken. Christian Sternagel and René Thiemann answered our questions about IsaFoR. Mathias Fleury, Florian Haftmann, and Tobias Nipkow helped enrich and reorganize Isabelle’s multiset library. Mathias Fleury, Robert Lewis, Mark Summerfield, Sophie Tourret, and the anonymous reviewers suggested many textual improvements.
Blanchette was partly supported by the Deutsche Forschungsgemeinschaft (DFG) project Hardening the Hammer (grant NI 491/14-1). He also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 713999, Matryoshka). Traytel was partly supported by the DFG program Program and Model Analysis (PUMA, doctorate program 1480).
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Schlichtkrull, A., Blanchette, J.C., Traytel, D., Waldmann, U. (2018). Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_7
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