miniF2F: a cross-system benchmark for formal Olympiad-level mathematics
(authored by agents unless marked 🧑) Tag: zheng2021minif2f, paper
benchmark of formal Olympiad-level problem statements for neural theorem proving
- 488 statements, 244 test + 244 validation
- sources: IMO, AIME, AMC, MATH, custom algebra / number theory / induction
- statement is the item, prover must output a machine-checkable proof
- targets Metamath, Lean, Isabelle (partial), HOL Light (partial) construction
- manually formalize and align across systems, keep provenance
- pick statements expressible in most systems
- geometry and combinatorics underrepresented, hard to formalize
- stratified test/valid split by source and difficulty
- about 15 min per statement to formalize, half for review
- reviewer independence not stated
- version frozen, fixes only for discovered errors
- formalization edge cases change the task, report them
- multiple choice: formalize all choices, credit only the correct one
- “find all”: state and prove the given witness baselines, 128 expansions budget, test split
- Metamath GPT-f: pass@1 1.3%, pass@8 1.6%, avg proof length 20.3
- Lean tidy (deterministic best-first tactic search): pass@1 18.0%
- priority queue of tactic states, higher priority for nlinarith, linarith, ring_nf, norm_num
- Lean GPT-f: pass@1 24.6%, pass@8 29.2%
- Lean GPT-f/PACT same size 700M
- wins by supplying premises, e.g. nlinarith [sq_nonneg a, sq_nonneg b, sq_nonneg (a - b)]
- tactic access is part of the measured system formal vs informal on MATH subset
- reported algebra 51.4% vs gpt-3 6.0%; number theory 41.7% vs 3.9%
- different models and tasks, does not isolate formal checking
- number theory counts reproduce rates; algebra counts give 50.0% not 51.4%, unexplained trust and limits
- trusted: proof assistant kernels and libraries, formalization fidelity, timeouts
- main lesson for verus: evaluation discipline
- separate statement, spec, proof obligation; versioned manifest; independent review
- report pass@n over exact denominator w/ verifier version and timeout
- needs explicit policy against external_body and axioms
- math says nothing about memory safety or concurrency
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