bkhtmm/openai-math-lemmas

OpenAI Math Lemmas

From one formal-math problem to 47 independently checkable Lean proof tasks.

We extracted 47 supporting lemmas from the reference proof of honeycomb-free-energy in FineEnvs/openai-math and packaged them as self-contained proof tasks. Each supplies the definitions and earlier proved lemmas needed to attempt one missing proof, retaining binary verification.

This is an early contribution from Desargues toward stronger open formal-reasoning models.

Separate lemma tasks let developers investigate which components their models can prove, where success is occasional, and where further work may help. Some may provide successful proof attempts even when the full theorem remains out of reach, making them candidates for smaller training objectives.

How a task works

Each task contains a Lean source prefix with one missing proof. The solver writes /workspace/Submission.lean using the source in instruction.md and replaces the single by sorry. Definitions, notation, and earlier proved lemmas are supplied; later declarations are omitted.

The inherited FineEnvs verifier returns 1 for an accepted proof of the unchanged statement and 0 for a rejected submission. Comparator checks statement identity, permitted axioms (propext, Quot.sound, Classical.choice), and Lean kernel replay. Infrastructure failures are reported as errors rather than proof failures.

All 47 targets support the reference proof of OAI.HoneycombForce.logPartition_tendsto. They describe components of that proof; they do not establish a unique decomposition or imply uniform difficulty.

What's included

• tasks/ — 47 Harbor task bundles with instructions, environment recipes, trusted challenges, verifiers, and reference archives for the oracle agent.
• registry.json — the Harbor task registry.
• manifest.parquet and manifest.json — task indexes with source, target, supplied context, task location, and validation information.
• runtime/snapshot.py — a helper for building the shared Daytona snapshot.
• validation.json — the scope and results of the existing validation.
• License files and NOTICE — licensing and attribution.

The viewer's train split indexes the 47 available tasks; it is not a designated training partition paired with a held-out evaluation set.

Run it

Install the tools and download the dataset:

pip install "harbor[daytona]>=0.24,<0.25" daytona huggingface_hub
hf download bkhtmm/openai-math-lemmas --repo-type dataset --local-dir openai-math-lemmas
cd openai-math-lemmas

Configure DAYTONA_API_KEY and DAYTONA_API_URL in your shell, then build the shared snapshot and run the reference solver for one task:

python runtime/snapshot.py
SNAP=$(python runtime/snapshot.py --print-name)

harbor run -p tasks -e daytona --ek snapshot_template_name="$SNAP" \
  -a oracle -i honeycomb-free-energy--oai-honeycombforce-mem-neighbors-iff-119adcf5c8

Validation

Check	Existing result
Local restored reference proofs and allowed axioms	47 / 47 pass
Aggregate Comparator statement, definition, axiom, and kernel checks	All 47 targets pass in one original-source prefix
Individual task Comparator and negative-submission checks	One task tested; its reference proof passes and five invalid submissions are rejected
Full Harbor execution, separate verifier, and live isolation	Not yet run

The aggregate Comparator check is separate from the 47 local proof replays; it is not 47 independent environment runs. See validation.json for the evidence summary and scope.

Notes

Earlier proofs are part of each task's supplied context. Performance therefore measures proving a lemma with those prerequisites, rather than discovering the whole proof strategy. All tasks come from one parent problem.

Do not mount the whole repository into a learner sandbox. Reference archives contain solutions, and later tasks' prefixes include earlier tasks' answers. Provide only the current task's learner-facing instructions and environment. Randomly splitting sibling tasks between training and evaluation can leak answers; the original reference proofs are also public.

Sources and license

Desargues packaged these subtasks from OpenAI's openai/math, building on the environments and verification infrastructure in FineEnvs/openai-math.

Component	Pinned version / revision
FineEnvs/openai-math	d7056fd31c19fd1a0aed0a0bc3e99026d412b2ca
openai/math	adc7f1241b42e322a6451854ab7e4b4c146bf78a
Lean	4.34.1
Mathlib	d13f23b723b8a846827a245b89c10fc7d3f11612
Comparator	d03acab154d269c06e60e4de7e4cc85deebff94b

Apache-2.0; see LICENSE, LICENSE-openai-math, and NOTICE. The Lean source is from openai/math (© OpenAI). This release redistributes proved prerequisite lemmas and selected reference proofs. It is an independent Desargues contribution, not an official OpenAI or FineEnvs release.