Enhancing Superposition Reasoning in Linear Real Arithmetic through Selection and Simplification

20 pages•Published: October 23, 2026

Johannes Schoisswohl, Laura Kovács, Konstantin Korovin and Andrei Voronkov

Abstract

The calculus ALASCA extends superposition-based saturation proving with reasoning in Uninterpreted Functions and Linear Real Arithmetic (UFLRA). As efficiency of saturation algorithms depend on literal selection, simplification, and redundancy elimination, this paper improves reasoning in Uflra by introducing theory-specific notions and methods for all of these techniques. The implementation of these methods in the first-order theorem prover Vampire shows substantial gains in every tested benchmark category, solving a number of problems previously unsolved by any system.

Keyphrases: automated reasoning, first order theorem proving, linear arithmetic, literal selection, real arithmetic, redundancy, smt, superposition

In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 167-186.

Links:	https://easychair.org/publications/paper/TCsRH
	https://doi.org/10.29007/9sfw

BibTeX entry

@inproceedings{LPAR-26:Enhancing_Superposition_Reasoning_Linear,
  author    = {Johannes Schoisswohl and Laura Kovács and Konstantin Korovin and Andrei Voronkov},
  title     = {Enhancing Superposition Reasoning in Linear Real Arithmetic through Selection and Simplification},
  booktitle = {Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning},
  editor    = {Erika Ábrahám and Nikolaj Bjørner and Michael Rawson},
  series    = {EPiC Series in Computing},
  volume    = {112},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/TCsRH},
  doi       = {10.29007/9sfw},
  pages     = {167-186},
  year      = {2026}}

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