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2017 | OriginalPaper | Chapter

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

Authors : Daniyar Itegulov, John Slaney, Bruno Woltzenlogel Paleo

Published in: Automated Deduction – CADE 26

Publisher: Springer International Publishing

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Abstract

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.

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previous chapter Theorem Proving for Metric Temporal Logic over the Naturals

next chapter WorkflowFM: A Logic-Based Framework for Formal Process Specification and Composition

Not to be confused with the homonymous calculus for linear rational inequalities [17].

In practice, optimizations (e.g. 1UIP) are used, and more sophisticated clauses, which are not just disjunctions of duals of the decision literals involved in the conflict, can be derived. But these optimizations are inessential to the focus of this paper.

Because of the isomorphism between implication graphs and subderivations in Conflict Resolution [25], the propagation depth is equal to the corresponding subderivation’s height, where initial axiom clauses and learned clauses have height 0 and the height of the conclusion of a unit-propagating resolution inference is \(k + 1\) where k is the maximum height of its unit premises.

The depth of constants and variables is zero and the depth of a complex term is \(k+1\) when k is the maximum depth of its proper subterms.

Raw experimental data are available at https://doi.org/10.5281/zenodo.293187.

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Title: Scavenger 0.1: A Theorem Prover Based on Conflict Resolution
Authors: Daniyar Itegulov
John Slaney
Bruno Woltzenlogel Paleo
Publisher: Springer International Publishing
Book: Automated Deduction – CADE 26
Print ISBN: 978-3-319-63045-8

Electronic ISBN: 978-3-319-63046-5

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-63046-5_21

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