---
license: apache-2.0
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
tags:
  - theorem-proving
  - formal-methods
  - lean4
size_categories:
  - 1K<n<10K
dataset_info:
  features:
  - {name: statement, dtype: string}
  - {name: proof, dtype: string}
  - {name: type, dtype: string}
  - {name: symbolic_name, dtype: string}
  - {name: library, dtype: string}
  - {name: filename, dtype: string}
  - {name: imports, list: string}
  - {name: deps, list: string}
  - {name: docstring, dtype: string}
  - {name: source_url, dtype: string}
  - {name: commit, dtype: string}
  splits:
  - {name: train, num_examples: 4557}
  config_name: default
configs:
- config_name: default
  data_files:
  - split: train
    path: data/train-*
---

# Lean4-FormalConjectures

Structured dataset from **formal-conjectures** — Google DeepMind formalized conjectures.

## Source

- Repository: https://github.com/google-deepmind/formal-conjectures
- Commit: `b9b8aa0fd6170e482798f7c78c163acacd40e083`
- Files: 896
- License: apache-2.0

## Schema

| Column | Type | Description |
|--------|------|-------------|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level `Require`/`Import` modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |

## Statistics

- Entries: 4,557
- With proof: 4,472 (98.1%)
- With docstring: 3,759 (82.5%)
- Libraries: 88

### By type

| Type | Count |
|---|---|
| theorem | 2,859 |
| def | 1,143 |
| lemma | 364 |
| abbrev | 81 |
| structure | 53 |
| instance | 24 |
| inductive | 15 |
| class | 13 |
| elab | 3 |
| macro | 2 |

## Example

```
S (S₀ : List ℤ) (n : ℕ) : List ℤ
match n with
  | 0 => S₀
  | n + 1 => (S S₀ n) ++ [Int.ofNat (k (S S₀ n))]
```

- type: def | symbolic_name: `Arxiv..S` | FormalConjectures/Arxiv/0912.2382/CurlingNumberConjecture.lean

## Use

Each declaration is split into a `statement` (signature/claim) and a `proof` (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via `deps`.

## Citation

```bibtex
@misc{lean4_formalconjectures_dataset,
  title  = {Lean4-FormalConjectures},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/google-deepmind/formal-conjectures, commit b9b8aa0fd617},
  url    = {https://huggingface.co/datasets/phanerozoic/Lean4-FormalConjectures}
}
```