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arXiv · 2605.21335

A Two-Watched Literal Scheme for First-Order Logic

Yasmine Briefs·Martin Bromberger·Tobias Gehl·Lorenz Leutgeb·Simon Schwarz·Christoph Weidenbach
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Abstract

The two-watched literal scheme, a core component of efficient CDCL (Conflict-Driven Clause Learning) implementations for propositional logic, is extended to first-order logic. Given a set of first-order clauses and a set of ground literals, our lifted two-watched literal scheme efficiently detects all propagating and false clauses with respect to the ground literals. We present the algorithm as a system of rules and prove its soundness and completeness. Additionally, we provide an implementation of the two-watched literal scheme, which outperforms a standard dynamic programming approach for detecting propagatable literals and conflicts, especially when dealing with long clauses.

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Yasmine Briefs, Martin Bromberger, Tobias Gehl, Lorenz Leutgeb, Simon Schwarz, Christoph Weidenbach. 2026-05-20. A Two-Watched Literal Scheme for First-Order Logic. https://arxiv.org/abs/2605.21335

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