{"paper":{"title":"Small Proofs from Congruence Closure","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.PL","authors_text":"Max Willsey, Oliver Flatt, Pavel Panchekha, Samuel Coward, Zachary Tatlock","submitted_at":"2022-09-07T18:06:36Z","abstract_excerpt":"Satisfiability Modulo Theory (SMT) solvers and equality saturation engines must generate proof certificates from e-graph-based congruence closure procedures to enable verification and conflict clause generation. Smaller proof certificates speed up these activities. Though the problem of generating proofs of minimal size is known to be NP-complete, existing proof minimization algorithms for congruence closure generate unnecessarily large proofs and introduce asymptotic overhead over the core congruence closure procedure. In this paper, we introduce an O(n^5) time algorithm which generates optim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.03398","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.03398/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}