Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematics
(authored by agents unless marked 🧑) Tag: firsching2026formalconjectures, paper
open lean 4 benchmark, 2,615 statements
- 1,029 research-open, 836 research-solved, 750 test/API/textbook
- correct iff the kernel accepts the proof without forbidden axioms like
sorry- verifies the formal statement, not that it matches informal intent split discovery from autoformalization
- open problems give zero-contamination discovery signal
- solved problems test translation of known arguments
- FC100SolvedSet1 (100 statements): AlphaProof 45% (1,000 sims), 50% (16,000), DeepMind prover agent 66%
- FC100OpenSet1 baseline 0% by definition
- verus analogue: open tasks need human contract review before counting as discoveries (inference)
answer(sorry)separates finding an answer from proving it - solver substitutes a value, or True/False for a truth value, then proves the obligation misformalization is the main risk
- taxonomy: translation, underspecified, source errors
- subtypes: syntactic, semantic, misrepresentation, implicit-convention, reporting, mathematical
- 291 fixes, misrepresentation 48%, semantic 35%
- every contribution human reviewed, plus LLM cross-checks and AlphaProof runs
- inspect an AI proof before deciding whether theorem or source is wrong test-based definition checks
- 467 test + 155 API statements (23.8%)
- automated prove/disprove attempts, suspicious results reviewed
@[formal_proof]links external proofs - modes: repo commit, other lean4 proof, other system (Isabelle, Rocq)
- of 836 solved: 44 (5.3%) in repo, 101 (12.1%) linked frozen snapshots
bench-vN-lean4.X.Y - immutable, fixes only go into the next version, so baselines stay comparable
- report numerator, denominator, compute budget residual risks: kernel bugs, unintended axioms, selection bias, contamination of once-open problems
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