---
license: apache-2.0
pretty_name: ProofWriter (The Cut)
tags:
- logical-reasoning
- proof-generation
configs:
- config_name: owa-att-noneg-d1
  data_files:
  - split: train
    path: owa-att-noneg-d1/train.parquet
  - split: val
    path: owa-att-noneg-d1/val.parquet
  - split: test
    path: owa-att-noneg-d1/test.parquet
- config_name: owa-att-noneg-d2
  data_files:
  - split: train
    path: owa-att-noneg-d2/train.parquet
  - split: val
    path: owa-att-noneg-d2/val.parquet
  - split: test
    path: owa-att-noneg-d2/test.parquet
- config_name: owa-att-noneg-d3
  data_files:
  - split: train
    path: owa-att-noneg-d3/train.parquet
  - split: val
    path: owa-att-noneg-d3/val.parquet
  - split: test
    path: owa-att-noneg-d3/test.parquet
- config_name: owa-att-noneg-d5
  data_files:
  - split: train
    path: owa-att-noneg-d5/train.parquet
  - split: val
    path: owa-att-noneg-d5/val.parquet
  - split: test
    path: owa-att-noneg-d5/test.parquet
- config_name: owa-att-neg-d1
  data_files:
  - split: train
    path: owa-att-neg-d1/train.parquet
  - split: val
    path: owa-att-neg-d1/val.parquet
  - split: test
    path: owa-att-neg-d1/test.parquet
- config_name: owa-att-neg-d2
  data_files:
  - split: train
    path: owa-att-neg-d2/train.parquet
  - split: val
    path: owa-att-neg-d2/val.parquet
  - split: test
    path: owa-att-neg-d2/test.parquet
- config_name: owa-att-neg-d3
  data_files:
  - split: train
    path: owa-att-neg-d3/train.parquet
  - split: val
    path: owa-att-neg-d3/val.parquet
  - split: test
    path: owa-att-neg-d3/test.parquet
- config_name: owa-att-neg-d5
  data_files:
  - split: train
    path: owa-att-neg-d5/train.parquet
  - split: val
    path: owa-att-neg-d5/val.parquet
  - split: test
    path: owa-att-neg-d5/test.parquet
- config_name: owa-rel-noneg-d1
  data_files:
  - split: train
    path: owa-rel-noneg-d1/train.parquet
  - split: val
    path: owa-rel-noneg-d1/val.parquet
  - split: test
    path: owa-rel-noneg-d1/test.parquet
- config_name: owa-rel-noneg-d2
  data_files:
  - split: train
    path: owa-rel-noneg-d2/train.parquet
  - split: val
    path: owa-rel-noneg-d2/val.parquet
  - split: test
    path: owa-rel-noneg-d2/test.parquet
- config_name: owa-rel-noneg-d3
  data_files:
  - split: train
    path: owa-rel-noneg-d3/train.parquet
  - split: val
    path: owa-rel-noneg-d3/val.parquet
  - split: test
    path: owa-rel-noneg-d3/test.parquet
- config_name: owa-rel-noneg-d5
  data_files:
  - split: train
    path: owa-rel-noneg-d5/train.parquet
  - split: val
    path: owa-rel-noneg-d5/val.parquet
  - split: test
    path: owa-rel-noneg-d5/test.parquet
- config_name: owa-rel-neg-d1
  data_files:
  - split: train
    path: owa-rel-neg-d1/train.parquet
  - split: val
    path: owa-rel-neg-d1/val.parquet
  - split: test
    path: owa-rel-neg-d1/test.parquet
- config_name: owa-rel-neg-d2
  data_files:
  - split: train
    path: owa-rel-neg-d2/train.parquet
  - split: val
    path: owa-rel-neg-d2/val.parquet
  - split: test
    path: owa-rel-neg-d2/test.parquet
- config_name: owa-rel-neg-d3
  data_files:
  - split: train
    path: owa-rel-neg-d3/train.parquet
  - split: val
    path: owa-rel-neg-d3/val.parquet
  - split: test
    path: owa-rel-neg-d3/test.parquet
- config_name: owa-rel-neg-d5
  data_files:
  - split: train
    path: owa-rel-neg-d5/train.parquet
  - split: val
    path: owa-rel-neg-d5/val.parquet
  - split: test
    path: owa-rel-neg-d5/test.parquet
- config_name: cwa-att-noneg-d1
  data_files:
  - split: train
    path: cwa-att-noneg-d1/train.parquet
  - split: val
    path: cwa-att-noneg-d1/val.parquet
  - split: test
    path: cwa-att-noneg-d1/test.parquet
- config_name: cwa-att-noneg-d2
  data_files:
  - split: train
    path: cwa-att-noneg-d2/train.parquet
  - split: val
    path: cwa-att-noneg-d2/val.parquet
  - split: test
    path: cwa-att-noneg-d2/test.parquet
- config_name: cwa-att-noneg-d3
  data_files:
  - split: train
    path: cwa-att-noneg-d3/train.parquet
  - split: val
    path: cwa-att-noneg-d3/val.parquet
  - split: test
    path: cwa-att-noneg-d3/test.parquet
- config_name: cwa-att-noneg-d5
  data_files:
  - split: train
    path: cwa-att-noneg-d5/train.parquet
  - split: val
    path: cwa-att-noneg-d5/val.parquet
  - split: test
    path: cwa-att-noneg-d5/test.parquet
- config_name: cwa-att-neg-d1
  data_files:
  - split: train
    path: cwa-att-neg-d1/train.parquet
  - split: val
    path: cwa-att-neg-d1/val.parquet
  - split: test
    path: cwa-att-neg-d1/test.parquet
- config_name: cwa-att-neg-d2
  data_files:
  - split: train
    path: cwa-att-neg-d2/train.parquet
  - split: val
    path: cwa-att-neg-d2/val.parquet
  - split: test
    path: cwa-att-neg-d2/test.parquet
- config_name: cwa-att-neg-d3
  data_files:
  - split: train
    path: cwa-att-neg-d3/train.parquet
  - split: val
    path: cwa-att-neg-d3/val.parquet
  - split: test
    path: cwa-att-neg-d3/test.parquet
- config_name: cwa-att-neg-d5
  data_files:
  - split: train
    path: cwa-att-neg-d5/train.parquet
  - split: val
    path: cwa-att-neg-d5/val.parquet
  - split: test
    path: cwa-att-neg-d5/test.parquet
- config_name: cwa-rel-noneg-d1
  data_files:
  - split: train
    path: cwa-rel-noneg-d1/train.parquet
  - split: val
    path: cwa-rel-noneg-d1/val.parquet
  - split: test
    path: cwa-rel-noneg-d1/test.parquet
- config_name: cwa-rel-noneg-d2
  data_files:
  - split: train
    path: cwa-rel-noneg-d2/train.parquet
  - split: val
    path: cwa-rel-noneg-d2/val.parquet
  - split: test
    path: cwa-rel-noneg-d2/test.parquet
- config_name: cwa-rel-noneg-d3
  data_files:
  - split: train
    path: cwa-rel-noneg-d3/train.parquet
  - split: val
    path: cwa-rel-noneg-d3/val.parquet
  - split: test
    path: cwa-rel-noneg-d3/test.parquet
- config_name: cwa-rel-noneg-d5
  data_files:
  - split: train
    path: cwa-rel-noneg-d5/train.parquet
  - split: val
    path: cwa-rel-noneg-d5/val.parquet
  - split: test
    path: cwa-rel-noneg-d5/test.parquet
- config_name: cwa-rel-neg-d1
  data_files:
  - split: train
    path: cwa-rel-neg-d1/train.parquet
  - split: val
    path: cwa-rel-neg-d1/val.parquet
  - split: test
    path: cwa-rel-neg-d1/test.parquet
- config_name: cwa-rel-neg-d2
  data_files:
  - split: train
    path: cwa-rel-neg-d2/train.parquet
  - split: val
    path: cwa-rel-neg-d2/val.parquet
  - split: test
    path: cwa-rel-neg-d2/test.parquet
- config_name: cwa-rel-neg-d3
  data_files:
  - split: train
    path: cwa-rel-neg-d3/train.parquet
  - split: val
    path: cwa-rel-neg-d3/val.parquet
  - split: test
    path: cwa-rel-neg-d3/test.parquet
- config_name: cwa-rel-neg-d5
  data_files:
  - split: train
    path: cwa-rel-neg-d5/train.parquet
  - split: val
    path: cwa-rel-neg-d5/val.parquet
  - split: test
    path: cwa-rel-neg-d5/test.parquet
---

# ProofWriter (The Cut)

A **selection** of `proofwriter-mirror`, not a transform of it: every row is a mirror row
restricted to one question, with the same schema and every value verbatim. What this dataset adds
is *which* rows and *in what order*, so a number measured on it can be read.

## What was kept

Of ProofWriter's six question strategies, two — **`proof` and `rconc`** — the only two the whole task ladder
can score, since a `proof` question has a derivation to recover and an `rconc` question's answer
is that none exists.

The other four are dropped, and the reason is measurable. In an open-world, negation-free theory
no negated atom is derivable, so **every** negative-polarity question is unentailed: audited
across all 40 mirror configs, the entailed rate on those rows is `0.000` in all ten `owa-noneg`
ones. Since the three `inv-*` strategies are exactly the negated half of the question set, half of
any raw split is answerable by *"if the statement says «not», answer False"*, with no reasoning at
all. It cannot be balanced away — there is no entailed negative-polarity row to balance against —
so it is trimmed.

`random` goes too: its failure chain is the bare `(FAIL)` at depth 0, a lookup refusal rather than
a search. Dropping it drops depth 0 with it, and with that the corpus's heaviest skew.

## How much, at which depth

Classes are **matched per depth**, so each split is 50 / 50 entailed / unentailed and chance is
exactly 0.5. Depth is first-class on both sides: for an unprovable question ProofWriter's `QDep`
is the depth the *failed* search reached — it equals the `failure.depth` witness on every
unprovable row of all 40 configs — so an `rconc` row at depth *k* demands the same traversal as a
`proof` row at depth *k*.

The corpus thins geometrically with depth, so an untapered split would be three-quarters shallow
and its aggregate would nearly restate depth 1. Allocation walks depths deepest-first: the deepest
cell is taken **whole**, and each shallower one gets **1.5x** its deeper neighbour's realized
count, floored and capped by availability.

The deep end is therefore bounded by the shelf, not by the recipe — on `owa-att-noneg-d5`, `val`
holds 8 pairs at depth 5 against 40 at depth 1. **Read a per-depth result with its n**, and do not
weigh the deepest point like the shallowest.

## Splits, and the order

| split | drawn from | meant for |
|---|---|---|
| `train` | mirror `train` | training |
| `val` | mirror `dev` | the curve during a run |
| `test` | mirror `test` | the reported number, read once |

All three share one allocation: a validation curve measures the training distribution only if both
are drawn from the same one.

**The row order is part of the dataset.** Rows are round-robined over (depth, class), so every
cell contributes once before any contributes twice and the classes stay within one row of each
other at every prefix — which means taking the first N rows is a fair sample at any N. Consumers
that truncate without shuffling (a training run's `num_examples`, say) are why it is published
this way rather than left to chance.

Which rows fill a cell depends on nothing but the corpus's own ids: the least-used theory first,
ties broken by `(theory_id, question_id)`. No seed, and no dependence on row order upstream.

- **Derived from:** `proofwriter-mirror` (itself a typed mirror of AI2's ProofWriter `V2020.12.3`).
- **License:** `apache-2.0`, inherited.
- Not affiliated with or endorsed by AI2; bundled here with attribution.

## Citation

ProofWriter — and the RuleTaker corpora it builds on — are AI2's work. Please cite them:

```bibtex
@inproceedings{tafjord-etal-2021-proofwriter,
    title = "{P}roof{W}riter: Generating Implications, Proofs, and Abductive
             Statements over Natural Language",
    author = "Tafjord, Oyvind and Dalvi, Bhavana and Clark, Peter",
    booktitle = "Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021",
    year = "2021",
    eprint = "2012.13048",
    archivePrefix = "arXiv",
}
```

```bibtex
@inproceedings{clark-etal-2020-transformers,
    title = "Transformers as Soft Reasoners over Language",
    author = "Clark, Peter and Tafjord, Oyvind and Richardson, Kyle",
    booktitle = "Proceedings of the 29th International Joint Conference on
                 Artificial Intelligence (IJCAI-20)",
    year = "2020",
    eprint = "2002.05867",
    archivePrefix = "arXiv",
}
```