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Updated: Aug 22, 2025

A Protocol for Functional Assessment of Whole-Protein Saturation Mutagenesis Libraries Utilizing High-Throughput Sequencing
Published on: July 3, 2016
A Comprehensive Framework for Saturation Theorem Proving
Uwe Waldmann1, Sophie Tourret1,2, Simon Robillard3
1Max-Planck-Institut für Informatik, Saarland Informatics Campus, Saarbrücken, Germany.
Abstract:
A crucial operation of saturation theorem provers is deletion of subsumed formulas. Designers of proof calculi, however, usually discuss this only informally, and the rare formal expositions tend to be clumsy. This is because the equivalence of dynamic and static refutational completeness holds only for derivations where all deleted formulas are redundant, but the standard notion of redundancy is too weak: A clause C does not make an instance redundant. We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution and superposition. The framework modularly extends redundancy criteria derived via a familiar ground-to-nonground lifting. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures so that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus within, for instance, an Otter or DISCOUNT loop. Our framework is mechanized in Isabelle/HOL.
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