{"id":"9f8827a8-53ac-4874-809c-4c25249af100","arxiv_id":"2606.29493","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Audit of five Lean theorem-proving benchmarks identifies 4,833 findings with 398 certified issues and shows dataset defects can inflate or deflate prover scores.","lead":"This paper audits five popular Lean theorem-proving benchmarks and surfaces 4,833 findings including 398 mechanically certified defects such as counterexamples and unsound axioms. Smart generalists should read it because unreliable benchmarks can mislead AI progress in formal mathematics and make reported improvements hard to trust.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly flags the possibility of undetected semantic mismatches, yet the headline claim only requires that the identified and mechanically verified defects affect scores, which the released checkers and corrected snapshots directly enable verification of. No adjustment to the ACCEPT verdict is warranted.","tokens_in":1709,"tokens_out":233,"duration_ms":18692,"concrete_test":"Re-run the released checkers on the five original benchmark snapshots and compare the output defect list against the paper's reported 398 certified issues; separately re-evaluate at least one prover on a released corrected subset to confirm the reported score delta direction and magnitude.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that 398 mechanically certified defects (counterexamples, vacuous theorems, unsound axioms) plus other semantic issues exist in five benchmarks and that corrected subsets show both inflation and deflation of prover scores. The argument is supported by corpus-scale static checkers, released artifacts, and explicit re-evaluation on corrected data; no internal inconsistency appears in the quantification or the demonstration of score impact.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper audits five widely used Lean theorem-proving benchmarks and their forks using corpus-scale static checkers, surfacing 4,833 findings including 398 mechanically certified issues (counterexamples, vacuous theorems, unsound axioms). It documents additional semantic defects (missing hypotheses, incomplete translations, Lean-specific hazards) and shows via re-evaluation on corrected subsets that defects can both inflate and deflate reported prover scores. The authors propose a fault taxonomy, automated checkers, and recall-oriented semantic audit prompts, releasing all artifacts at the linked GitHub repository.","tokens_in":1764,"tokens_out":346,"duration_ms":23212,"significance":"If the results hold, the work is significant for LLM-assisted theorem proving because it supplies mechanically verified evidence of benchmark defects together with explicit demonstrations of score impact on corrected data. The open release of checkers, audit prompts, and corrected dataset snapshots directly supports reproducibility and better dataset construction practices in the field.","major_comments":[],"minor_comments":[{"comment":"The abstract states 4,833 findings with 398 mechanically certified issues, but the main text would benefit from an explicit table or section breaking down the 398 issues by type and by benchmark to improve traceability.","section":null},{"comment":"In the evaluation on corrected subsets, the demonstration of both inflation and deflation is clear, but adding statistical measures (e.g., confidence intervals on score deltas) would strengthen the quantitative claims without altering the central argument.","section":null},{"comment":"The fault taxonomy is introduced as a contribution; a short comparison table relating it to prior informal-benchmark taxonomies would help readers situate the new categories.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive summary of our work and the recommendation of minor revision. We will incorporate any minor improvements in the revised version.","responses":[],"tokens_in":1222,"tokens_out":48,"duration_ms":13848,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that five popular Lean theorem-proving benchmarks contain hundreds of defects that static checkers can catch mechanically, including 398 certified cases like counterexamples, vacuous theorems, and unsound axioms, and that re-running on corrected subsets shows both score inflation and deflation.\n\nWhat is new is the combination of corpus-scale checkers, the specific certified counts, the fault taxonomy, and the public corrected snapshots plus re-evaluation data. The work does well by grounding the defect claims in Lean kernel verification rather than manual judgment alone and by shipping the tools so others can apply them. The demonstration that defects move scores in both directions is the practical payoff.\n\nThe softer part is that semantic issues such as missing hypotheses or incomplete translations still rely on prompts and human review in places, so the checkers may miss some mismatches that only careful reading would catch; the paper is open about this limit. The exact fraction of overall score change across every benchmark is shown only on subsets, which leaves the full magnitude a bit open but does not undermine the existence of the problem.\n\nThis is for anyone building, using, or citing Lean-based theorem-proving benchmarks. It gives concrete ways to make evaluation more reliable.\n\nSend it to peer review; the artifacts and mechanical evidence make the claims checkable and the fixes actionable.","headline":"The paper finds 398 mechanically certified defects across five Lean benchmarks and shows they distort prover scores on corrected subsets, with released checkers and snapshots.","tokens_in":2245,"tokens_out":342,"would_cite":true,"duration_ms":19361,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Defects in five widely used Lean theorem-proving benchmarks can both inflate and deflate reported prover scores.","keywords":["Lean theorem proving","benchmark defects","formal verification","LLM-assisted proving","evaluation failures","dataset quality","static checkers","fault taxonomy"],"falsifier":"If prover success rates on the corrected dataset snapshots remain statistically indistinguishable from rates on the original benchmarks, that would show the identified defects do not affect reported scores.","tokens_in":2616,"feed_emoji":"⚠️","tokens_out":629,"duration_ms":31140,"temperature":0.7,"pith_summary":"The paper audits five popular Lean benchmarks for theorem proving and finds 4,833 findings from static checkers, including 398 mechanically certified issues such as counterexamples, vacuous theorems, and unsound axioms. These defects exist because the Lean kernel verifies only that a proof matches its formal statement, not that the statement matches the intended informal problem or that evaluation harnesses resist trivial solutions. On corrected subsets of the datasets, prover performance scores change in both directions. The authors supply a fault taxonomy, automated checkers, and recall-oriented semantic audit prompts to support more reliable benchmark construction.","feed_headline":"Lean benchmarks contain 398 certified defects that skew prover scores","feed_subtitle":"Audits find counterexamples and unsound axioms that both inflate and deflate performance on corrected subsets.","key_machinery":"Corpus-scale static checkers that detect counterexamples, vacuous theorems, and unsound axioms, together with a proposed fault taxonomy for formal mathematics datasets.","core_discovery":"Five widely used Lean theorem-proving benchmarks and their forks contain 4,833 findings surfaced by corpus-scale static checkers, of which 398 are mechanically certified issues including counterexamples, vacuous theorems, and unsound axioms, plus semantic defects such as missing hypotheses, problem simplification, incomplete translations, and Lean-specific hazards; these defects cause reported prover scores both to increase and to decrease when measured on corrected subsets, showing that evaluation harnesses are not robust to trivial or adversarial solutions.","pith_inferences":["Analogous defects are likely present in theorem-proving benchmarks for formal systems other than Lean.","Human review will probably remain necessary to catch semantic mismatches the checkers do not surface.","Widespread use of the checkers could make cross-paper comparisons of prover performance more reliable."],"forward_implications":["Corrected benchmark subsets produce different prover performance scores than the original versions.","Evaluation harnesses require design changes to resist trivial and adversarial solutions.","Future formal math datasets can use the released checkers and standards to reduce similar defects.","Semantic audit prompts can surface additional issues beyond those found by static analysis."],"fun_headline_variants":["398 certified defects skew prover scores in Lean benchmarks","Lean theorem benchmarks contain hidden counterexamples","Unsound axioms plague five Lean proving benchmarks","Defects inflate and deflate scores on corrected subsets","Semantic defects undermine Lean formal math benchmarks"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The five audited benchmarks and the static checkers together capture the main sources of evaluation failure without missing important semantic mismatches that only human review would detect.","fun_headline_variants_meta":{"raw":{"variants":["398 certified defects skew prover scores in Lean benchmarks","Lean theorem benchmarks contain hidden counterexamples","Unsound axioms plague five Lean proving benchmarks","Defects inflate and deflate scores on corrected subsets","Semantic defects undermine Lean formal math benchmarks"]},"model":"grok-4.3","cost_usd":0.004976,"raw_usage":{"total_tokens":2440,"prompt_tokens":684,"num_sources_used":0,"completion_tokens":64,"cost_in_usd_ticks":49762000,"prompt_tokens_details":{"text_tokens":684,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1692,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":684,"tokens_out":64,"duration_ms":15526,"temperature":1.0,"reasoning_tokens":1692,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T06:54:23.070139+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"If prover success rates on the corrected dataset snapshots remain statistically indistinguishable from rates on the original benchmarks, that would show the identified defects do not affect reported scores.","supporting_citations":[],"review_version":1}