{"paper":{"title":"Stress-Testing the Reasoning Competence of LLMs With Proofs Under Minimal Formalism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Frontier LLMs perform well on foundational proof tasks but fail at those requiring global combinatorial reasoning or low-level proof synthesis.","cross_cats":["cs.AI"],"primary_cat":"cs.LO","authors_text":"Konstantine Arkoudas, Serafim Batzoglou","submitted_at":"2026-04-07T01:19:41Z","abstract_excerpt":"We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof gap-filling. Tasks are expressed in minimal formal notation, especially NDL, a compact natural-deduction language that fits in short prompts and supports precise, auditable verification. This yields mechanical, reproducible, and fine-grained evaluation rather than judgments by humans or LLMs. ProofGrid covers a calibrated difficulty spectrum, from foundational reasoni"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Frontier models perform well on several foundational tasks, yet difficult tasks, especially those requiring global combinatorial reasoning or low-level proof synthesis, remain far from solved.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That success or failure on these minimal-formalism proof tasks provides a meaningful signal of general reasoning competence independent of domain knowledge, solver delegation, or long-context artifacts.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ProofGrid is a new benchmark for LLM reasoning that uses machine-checkable proofs in minimal formal notation, revealing progress on basic tasks but major gaps in complex combinatorial and synthesis reasoning.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Frontier LLMs perform well on foundational proof tasks but fail at those requiring global combinatorial reasoning or low-level proof synthesis.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7da9e1e09eb38dc5827baded10d0b7655c84c536e5613372a3b31986e76e63d7"},"source":{"id":"2605.12524","kind":"arxiv","version":1},"verdict":{"id":"606dcf7d-7425-41b4-86c4-43fed6c3f513","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:59:21.683069Z","strongest_claim":"Frontier models perform well on several foundational tasks, yet difficult tasks, especially those requiring global combinatorial reasoning or low-level proof synthesis, remain far from solved.","one_line_summary":"ProofGrid is a new benchmark for LLM reasoning that uses machine-checkable proofs in minimal formal notation, revealing progress on basic tasks but major gaps in complex combinatorial and synthesis reasoning.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That success or failure on these minimal-formalism proof tasks provides a meaningful signal of general reasoning competence independent of domain knowledge, solver delegation, or long-context artifacts.","pith_extraction_headline":"Frontier LLMs perform well on foundational proof tasks but fail at those requiring global combinatorial reasoning or low-level proof synthesis."},"references":{"count":143,"sample":[{"doi":"","year":2003,"title":"Karl Popper: Critical Assessments of Leading Philosophers , publisher =","work_id":"978160ee-d5ed-492c-8342-916ddfc76021","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Journal for General Philosophy of Science , year =","work_id":"f4e27fbb-a78d-4e44-96ad-521379df3b72","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Argumentation , year =","work_id":"dcef650e-211e-410e-bbe6-627866aa361b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Item Response Theory: Principles and Applications , author=. 1985 , publisher=","work_id":"06c55e58-0592-453b-be05-385031c4899c","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Handbook of Item Response Theory Modeling: Applications to Typical Performance Assessment , publisher =","work_id":"62f9f4a0-86f9-494c-b4e2-139368fecaab","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":143,"snapshot_sha256":"29e69991e019d7280ce36baaf4829cb7437869946a239f9f2074208f0339baef","internal_anchors":7},"formal_canon":{"evidence_count":1,"snapshot_sha256":"3f639379e1124ddb18d392e7d83844f790967d8b8a17a7f524cd246b51938013"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}