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

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:

{
  "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