Datasets:

scicraft
/

LeanCat

Lean toolchain: leanprover/lean4:v4.19.0
Mathlib dependency: v4.19.0, pinned through lakefile.lean and lake-manifest.json
Build command: lake build

Reviewers and users should run all checks from the repository root.

Task Definition

Each task is a Lean file in CAT_statement/S_XXXX.lean paired with a natural-language statement in problems/XXXX.md and metadata in metadata.json.

A task is solved when a system replaces the target sorry placeholder or placeholders with Lean code and the resulting file is accepted by Lean under the pinned environment.

Valid Proof Criteria

A submitted proof is valid only if all of the following hold:

The corresponding Lean file compiles with Lean 4.19.0 and Mathlib v4.19.0.
The theorem statement, local definitions, imports, namespaces, universes, and assumptions are not changed in a way that weakens or changes the intended task.
The file contains no sorry, admit, axiom, or unsafe additions used to bypass proof obligations.
No new external dependencies are introduced unless the evaluation setting explicitly permits them.
The proof preserves the intended mathematical meaning of the task.

Compilation alone is not sufficient if a system changes the target statement or shadows key definitions to make a different theorem easier.

Recommended Reporting

Report results as raw counts and percentages over the 100 tasks. For small splits, report raw counts prominently because one solved High-difficulty task is 2.5 percentage points.

For pass@k settings, a task is counted as solved if at least one of the k independent attempts satisfies the valid proof criteria.

For interactive or retrieval-augmented settings, report:

input form: formal statement only, natural language only, or both;
retrieval access and corpus;
maximum refinement iterations;
generation budget;
verification timeout;
total wall-clock or service budget when available.

The paper experiments use a 300-second verification timeout per attempt unless otherwise stated.

Evaluation Drivers

This artifact includes two lightweight drivers. Both read the paired problems/XXXX.md and CAT_statement/S_XXXX.lean files, call an OpenAI-compatible chat-completions endpoint, extract Lean code from the response, and check the candidate with lake env lean.

Configure the API with environment variables or command-line flags:

Windows PowerShell:

$env:OPENAI_API_KEY="your_key"
$env:OPENAI_BASE_URL="https://api.openai.com/v1"

Linux/macOS:

export OPENAI_API_KEY="your_key"
export OPENAI_BASE_URL="https://api.openai.com/v1"

Static pass@k:

python scripts/passk.py --start 1 --end 100 --model gpt-5.2 -k 4

LeanBridge-style generate-verify-refine:

python scripts/leanbridge.py --start 1 --end 100 --model gpt-5.2 --max-iterations 4

By default, leanbridge.py uses the local LeanExplore backend:

pip install lean-explore[local]
lean-explore data fetch
python scripts/leanbridge.py --start 1 --end 100 --model gpt-5.2 --search-backend local

The hosted LeanExplore API can be selected with --search-backend api, but the local backend is recommended when the hosted API is unavailable. To run the verify-refine loop without retrieval, use --search-backend none. For custom retrievers, use --search-backend command --search-command "python path/to/search.py"; the command receives a query on stdin and writes retrieved Mathlib context to stdout.

For local LeanExplore, the service is created once per Python process and reused for all queries to avoid repeatedly loading the local indices and models. The script prints progress logs with a [LeanCat] prefix, including search, LLM, and Lean verification stages. The logs do not print API keys.

Outputs are written under results/ by default. Use --resume to skip existing result files.

Dataset Integrity Check

Run:

python scripts/validate_dataset.py

This checks the expected file counts, metadata consistency, import coverage, basic statement shape, and absence of root-level PDF files in the anonymized artifact.