---
license: other
license_name: mixed-apache-2.0-and-mit
license_link: LICENSE.md
pretty_name: ARB lean-proofs data packet
task_categories:
- text-generation
tags:
- lean4
- theorem-proving
- mathlib
size_categories:
- 100K<n<1M
---

# ARB lean-proofs data packet

The data packet of the `lean-proofs` task of applied-rsi-bench (Thoughtful-Lab): a training
pool of Lean 4 statements and proofs, and the case image's Mathlib search index. Nothing here
is a test or dev problem of the task.

## Files

| File | What | sha256 |
|---|---|---|
| `L.tar.gz` | The training pool (revision 2: the 16-gram rule added to the decontamination), in ARB's raw corpus format: `PACKET.json` (schema 2), `README.md` and three JSON Lines files | `1f8262e6c3bf8ebda805d1db1950c929068b435be0369af3c0133a78f335e5f9` |
| `mathlib-names-v4.27.0.tsv.gz` | The `search_mathlib` index: every declaration that `import Mathlib` and two FormalConjectures modules bring (Lean v4.27.0, Mathlib `a3a10db0`), without Lean's internal names and the Lean and Lake libraries, one line each: name, module, type as Lean prints it; 408,413 lines | `47caaf6157254417b7a3410d4168325750a8efc262f5467c97a433b79d6b5f67` (uncompressed: `76c29a0c9d5a6766a2ebc5d7277982874317fd5d460795ecf3ee6c2dc0b0f10b`) |

## The training pool

Each line of the JSON Lines files: `source`, `id`, `formal_statement`, `informal_statement`,
`proof` (a whole Lean file, or null), `lean` (the Lean version the source wrote it for).

| File | Source | Revision | License | Rows | With a proof | Removed |
|---|---|---|---|---|---|---|
| `lean_workbook.jsonl` | [internlm/Lean-Workbook](https://huggingface.co/datasets/internlm/Lean-Workbook) | `2e066e310b2c6d2c27616927ae131f82901c8f1c` | Apache-2.0 | 139,974 | 12,803 | 240 |
| `lean_workbook_proofs.jsonl` | [Goedel-LM/Lean-workbook-proofs](https://huggingface.co/datasets/Goedel-LM/Lean-workbook-proofs) | `b731852af8d8ab11498fda27bce9020738c01c59` | MIT | 29,658 | 29,658 | 92 |
| `numinamath_lean.jsonl` | [AI-MO/NuminaMath-LEAN](https://huggingface.co/datasets/AI-MO/NuminaMath-LEAN) | `51fa67f1f647ae1ecd81eef9f19306aa8a7b3a94` | Apache-2.0 | 103,654 | 9,302 | 501 |

The rows are the sources' own, renamed to one schema. Lean Workbook's rows have no id: the
theorem's name (`lean_workbook_<n>`) is the id, the one Lean-workbook-proofs names, and a
Lean-workbook-proofs row has its Lean Workbook statement. NuminaMath-LEAN's proof is its
`formal_ground_truth` when `ground_truth_type` is `complete` and it has no `sorry`. The rows
were written for Lean v4.8 to v4.15; many statements and proofs do not compile on v4.27.0
as they are.

## Decontamination

Every row that matches a problem of the task is removed: all of miniF2F (google-deepmind/miniF2F
`f0a20e14`: 244 test, 256 valid) and all 312 problems of IndiMathBench (prmbiy/IndiMathBench
`0eac2a55`), test and dev. A row matches when its formal statement (comments, imports, theorem
names, the final `sorry` and whitespace removed) or its informal statement (lowercased, letters
and digits only, LaTeX's `\dfrac`/`\tfrac` read as `\frac`, `\left`/`\right` left out) equals
the problem's; when it shares at least 50 % of the informal word 5-grams or 60 % of the formal
token 5-grams (Jaccard); or when it holds at least 10 % of the problem's word 16-grams (the
problem as its informal statement, then its Lean statement). 833 rows were removed, matching
359 problems (259 of miniF2F, mostly NuminaMath-LEAN's copies of MATH and AMC problems; 100 of
IndiMathBench). ARB's 16-gram probe then finds 0 of the task's 490 test problems with 25 % or
more of their 16-grams in the pool. The builder is `tasks/lean-proofs/data_packet/build.py` in applied-rsi-bench;
its `decontamination.json` lists the removed rows.

## Licenses

The pool keeps its sources' licenses: Lean Workbook and NuminaMath-LEAN are Apache-2.0,
Lean-workbook-proofs is MIT (see `LICENSE.md`). The index is derived from Mathlib, Lean 4 and
FormalConjectures, all Apache-2.0.