Datasets:

phanerozoic
/

Lean4-FormalConjectures

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

@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}
}