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https://github.com/openai/miniF2F

Formal to Formal Mathematics Benchmark
https://github.com/openai/miniF2F

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Formal to Formal Mathematics Benchmark

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README 

        
# MiniF2F



MiniF2F is a formal mathematics benchmark (translated across multiple formal systems) consisting of

exercise statements from olympiads (AMC, AIME, IMO) as well as high-school and undergraduate maths

classes.



The goal of the project is to provide a shared benchmark to evaluate and directly compare automated

theorem proving systems based on the formal systems targeted, initially **Lean**, and **Metamath**

(targeting also **Hol Light** and

**Isabelle**).



The benchmark (released under permissive licenses (MIT for Metamath, Apache for Lean)) is a work in

progress and contributions are welcome and encouraged through pull requests.



## Citation



The benchmark is described in detail in the following [pre-print](https://arxiv.org/abs/2109.00110):

```

@article{zheng2021minif2f,

  title={MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics},

  author={Zheng, Kunhao and Han, Jesse Michael and Polu, Stanislas},

  journal={arXiv preprint arXiv:2109.00110},

  year={2021}

}

```



## Statistics



|           | Test | Valid |

|:---------:|:----:|:-----:|

|   Lean    |  244 |  244  |

| Metamath  |  244 |  244  |

| Isabelle  |  244 |  244  |

| Hol Light |  165 |  165  |



## Structure



Each problem is represented by a unique name and a file for each of the formal systems we target.

Each file consists at minima in the problem statement and optionally one or more example proofs

associated with it. The benchmark is divided in two splits:



- `valid`: validation set that can be used while designing automated theorem proving systems

  (early-stopping, reinforcement learning, data-augmentation, curriculum design, ...).

- `test`: held-out test set reserved for final evaluation.



Naming conventions are still a work in progress. Olympiads problems are generally named after their

competition year and problem number (eg. `imo-1990-p3` or `aime-1983-p2`). Problems coming from a

particular dataset (eg the [MATH](https://arxiv.org/abs/2103.03874) dataset) are named to ease their

retrieval (eg. `mathd-algebra-125`). Other problems are prefixed by a category hint and a unique

name in the style of Metamath naming conventions (eg. `induction-11div10tonmn1ton`).



Each exercise file complies to the following system-specific conventions.



### Lean



To install the project make sure you have [elan](https://github.com/leanprover/elan) installed,

then in the directory where you want the project installed run:



```

git clone https://github.com/openai/miniF2F

cd miniF2F

leanpkg configure

leanpkg build

```



Since having one file per statement causes slowness in Lean parsing stage, all Lean statements are

exceptionally aggregated in two files (`valid.lean` and `test.lean`). These files contain a list of

the problem statements defined as `theorem`s. Optionally, proofs for these statements are provided

as well as potential lemmas to support the ground-truth proof.



No `theorem` should appear that do not correspond to a problem statement; use `lemma` instead.



Please use `lean/scripts/lint_style.py` to check all the statements pass the linter. You can also

make use of `lean/scripts/simple_formatter.sh` to enforce a few basic formatting rules.



The `lean` folder is released under the Apache License (so that it is aligned with Lean's mathlib

license).



### Metamath



Each file contains the problem statement with the same name as the problem unique name. The

statement is commented (using Metamath convention) if provided without proof.



The `metamath` folder is released under the MIT License.



### HOL Light



Each file contains the problem statement defined as a HOL Light term

whose name must match the file name.



The `hollight` folder is released under the FreeBSD License.



### Isabelle



Each file contains the problem statement defined as a theorem

whose name must match the file name, optionally with a proof for it as well as the necessary

imports.



The `isabelle` folder is released under the Apache License.



## Code of Conduct and Contributions



MiniF2F is meant to serve as a shared and useful resource for the machine learning community working

on formal mathematics. 



There is no obligation tied with the use and reporting of a result based on miniF2F. But if you're

using it and discovering new proofs (manually or automatically) please contribute them back to the

benchmark.



All contributions, such as new statements for later versions, addition of missing statements for

existing versions, bug fixes, additional proofs are all welcome.



## Versioning



A version of miniF2F is defined by a frozen set of statements. The goal for each version is to get

full coverage on all formal systems for that version even if that might not be the case when the

version is frozen.



When reporting a result based on miniF2F please always specify the version you used. The current

version is `v1`, frozen as of August 2021, including 244 statements (fully translated to Lean and

Metamath but still WIP in other formal systems).



Each version will live in its own branch to allow later additions of translated statements or fixes

to existing statements as needed. The `main` branch remains reserved for active development and

should not be used when reporting results.



### Active version



- Version: `v1`

- Freeze date: August 2021

- Branch: [v1](https://github.com/openai/miniF2F/tree/v1)