# Faster Certified Symmetry Breaking Using Orders With Auxiliary Variables

arXiv: https://arxiv.org/abs/2511.16637 · HTML: https://mlsanity.com/paper/2511.16637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 39 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs](https://mlsanity.com/paper/2209.12185/) (2022)
- [Efficient Certified RAT Verification](https://mlsanity.com/paper/1612.02353/) (2016)
- [Certified Symmetry and Dominance Breaking for Combinatorial Optimisation](https://mlsanity.com/paper/2203.12275/) (2022)
- [satsuma: Structure-based Symmetry Breaking in SAT](https://mlsanity.com/paper/2406.13557/) (2024)
- [The strength of the dominance rule](https://mlsanity.com/paper/2406.13657/) (2024)

## Abstract (arXiv)

Symmetry breaking is a crucial technique in modern combinatorial solving, but it is difficult to be sure it is implemented correctly. The most successful approach to deal with bugs is to make solvers certifying, so that they output not just a solution, but also a mathematical proof of correctness in a standard format, which can then be checked by a formally verified checker. This requires justifying symmetry reasoning within the proof, but developing efficient methods for this has remained a long-standing open challenge. A fully general approach was recently proposed by Bogaerts et al. (2023), but it relies on encoding lexicographic orders with big integers, which quickly becomes infeasible for large symmetries. In this work, we develop a method for instead encoding orders with auxiliary variables. We show that this leads to orders-of-magnitude speed-ups in both theory and practice by running experiments on proof logging and checking for SAT symmetry breaking using the state-of-the-art satsuma symmetry breaker and the VeriPB proof checking toolchain.