| --- |
| license: apache-2.0 |
| task_categories: |
| - text-generation |
| language: |
| - en |
| tags: |
| - lean4 |
| - theorem-proving |
| - formal-mathematics |
| - verification |
| - math |
| size_categories: |
| - 1M<n<10M |
| configs: |
| - config_name: compfiles |
| data_files: |
| - split: train |
| path: data/compfiles/train-*.parquet |
| - config_name: deepseek_prover |
| data_files: |
| - split: train |
| path: data/deepseek_prover/train-*.parquet |
| - config_name: deepseek_proverbench |
| data_files: |
| - split: train |
| path: data/deepseek_proverbench/train-*.parquet |
| - config_name: formal_conjectures |
| data_files: |
| - split: train |
| path: data/formal_conjectures/train-*.parquet |
| - config_name: formalmath |
| data_files: |
| - split: train |
| path: data/formalmath/train-*.parquet |
| - config_name: goedel_minif2f |
| data_files: |
| - split: train |
| path: data/goedel_minif2f/train-*.parquet |
| - config_name: goedel_mobench |
| data_files: |
| - split: train |
| path: data/goedel_mobench/train-*.parquet |
| - config_name: goedel_pset |
| data_files: |
| - split: train |
| path: data/goedel_pset/train-*.parquet |
| - config_name: goedel_test |
| data_files: |
| - split: train |
| path: data/goedel_test/train-*.parquet |
| - config_name: hf_lean_workbook |
| data_files: |
| - split: train |
| path: data/hf_lean_workbook/train-*.parquet |
| - config_name: hf_minif2f_lean4 |
| data_files: |
| - split: train |
| path: data/hf_minif2f_lean4/train-*.parquet |
| - config_name: hf_minif2f_v2 |
| data_files: |
| - split: train |
| path: data/hf_minif2f_v2/train-*.parquet |
| - config_name: hf_tonic_minif2f |
| data_files: |
| - split: train |
| path: data/hf_tonic_minif2f/train-*.parquet |
| - config_name: lean_proofs |
| data_files: |
| - split: train |
| path: data/lean_proofs/train-*.parquet |
| - config_name: lean_workbook_full |
| data_files: |
| - split: train |
| path: data/lean_workbook_full/train-*.parquet |
| - config_name: matholympiadbench |
| data_files: |
| - split: train |
| path: data/matholympiadbench/train-*.parquet |
| - config_name: nemotron_proofs |
| data_files: |
| - split: train |
| path: data/nemotron_proofs/train-*.parquet |
| - config_name: numinamath_lean |
| data_files: |
| - split: train |
| path: data/numinamath_lean/train-*.parquet |
| - config_name: proofnet |
| data_files: |
| - split: train |
| path: data/proofnet/train-*.parquet |
| - config_name: putnam2025 |
| data_files: |
| - split: train |
| path: data/putnam2025/train-*.parquet |
| - config_name: putnam_bench |
| data_files: |
| - split: train |
| path: data/putnam_bench/train-*.parquet |
| dataset_info: |
| features: |
| - name: id |
| dtype: string |
| - name: source |
| dtype: string |
| - name: formal_statement |
| dtype: string |
| - name: header |
| dtype: string |
| - name: lean4_code |
| dtype: string |
| - name: has_proof |
| dtype: bool |
| - name: proof_body |
| dtype: string |
| - name: natural_language |
| dtype: string |
| - name: lean_version |
| dtype: string |
| - name: split |
| dtype: string |
| - name: tags |
| sequence: string |
| - name: category |
| dtype: string |
| - name: verification |
| dtype: string |
| - name: v4210_is_valid |
| dtype: bool |
| - name: v4210_compiles |
| dtype: bool |
| - name: v4210_has_sorry |
| dtype: bool |
| - name: v4210_latency_s |
| dtype: float64 |
| --- |
| |
| # ai4math-lean |
|
|
| 21 Lean 4 formal mathematics datasets with machine-verified labels. |
|
|
| Every problem has been verified against lean-server v4.21.0 on UVA's HPC cluster. |
| Results are embedded in each row as both structured `verification` JSON and flattened convenience columns. |
|
|
| ## Quick Start |
|
|
| ```python |
| from datasets import load_dataset |
| |
| # Load a single dataset |
| ds = load_dataset("charliemeyer2000/ai4math-lean", "deepseek_prover") |
| |
| # Load a large dataset with streaming |
| ds = load_dataset("charliemeyer2000/ai4math-lean", "goedel_pset", streaming=True) |
| |
| # Filter to valid proofs |
| valid = ds.filter(lambda x: x["v4210_is_valid"] == True) |
| |
| # Filter to RL targets (compiles but no proof) |
| rl = ds.filter(lambda x: x["v4210_compiles"] and not x["has_proof"]) |
| ``` |
|
|
| ## Totals |
|
|
| | Metric | Count | |
| |--------|-------| |
| | Total problems | 3,394,310 | |
| | With proofs (SFT) | 1,273,472 | |
| | Valid on v4.21.0 | 352,065 | |
|
|
| ## Datasets |
|
|
| | Dataset | Problems | Proofs | Valid v4.21.0 | |
| |---------|----------|--------|---------------| |
| | compfiles | 297 | 259 | 67 | |
| | deepseek_prover | 27,503 | 27,503 | 27,126 | |
| | deepseek_proverbench | 325 | 0 | 0 | |
| | formal_conjectures | 618 | 13 | 13 | |
| | formalmath | 5,560 | 5,556 | 2 | |
| | goedel_minif2f | 244 | 0 | 0 | |
| | goedel_mobench | 360 | 0 | 0 | |
| | goedel_pset | 1,732,594 | 263,589 | 9,755 | |
| | goedel_test | 8 | 0 | 0 | |
| | hf_lean_workbook | 29,750 | 29,750 | 29,208 | |
| | hf_minif2f_lean4 | 231 | 0 | 0 | |
| | hf_minif2f_v2 | 488 | 0 | 0 | |
| | hf_tonic_minif2f | 488 | 0 | 0 | |
| | lean_proofs | 98 | 97 | 15 | |
| | lean_workbook_full | 140,214 | 0 | 0 | |
| | matholympiadbench | 360 | 0 | 0 | |
| | nemotron_proofs | 1,349,950 | 915,078 | 285,867 | |
| | numinamath_lean | 104,155 | 31,615 | 0 | |
| | proofnet | 371 | 0 | 0 | |
| | putnam2025 | 24 | 12 | 12 | |
| | putnam_bench | 672 | 0 | 0 | |
| |
| ## Schema |
| |
| Each row contains: |
| |
| | Field | Type | Description | |
| |-------|------|-------------| |
| | `id` | string | Unique problem identifier | |
| | `source` | string | Dataset source name | |
| | `formal_statement` | string | Lean 4 theorem statement (no proof body) | |
| | `header` | string | Import/setup code | |
| | `lean4_code` | string | Full runnable Lean 4 code | |
| | `has_proof` | bool | True if contains a real proof (not sorry) | |
| | `proof_body` | string? | Proof tactic block (if has_proof) | |
| | `natural_language` | string? | NL problem statement (if available) | |
| | `lean_version` | string? | Original Lean toolchain version | |
| | `split` | string? | train/test/val split | |
| | `tags` | list[string] | Tags (topic, difficulty, etc.) | |
| | `category` | string? | Math category | |
| | `verification` | string (JSON) | Full verification results per Lean version | |
| | `v4210_is_valid` | bool? | True=valid, False=errors/sorry, None=timeout | |
| | `v4210_compiles` | bool | Whether the code compiled (is_valid is not None) | |
| | `v4210_has_sorry` | bool? | Whether sorry was detected | |
| | `v4210_latency_s` | float? | Verification wall time in seconds | |
| |
| ## Verification Details |
| |
| The `verification` column contains a JSON string mapping Lean versions to results: |
| |
| ```json |
| { |
| "v4.21.0": { |
| "is_valid": false, |
| "has_sorry": true, |
| "errors": [], |
| "timeout_s": 600.0, |
| "latency_s": 34.59, |
| "verified_at": "2026-03-26T21:57:47Z" |
| } |
| } |
| ``` |
| |
| ## License |
|
|
| Apache 2.0 |
|
|
