---
license: cc-by-nc-sa-4.0
language:
- en
pretty_name: ProofRank Qualitative Disagreement Examples
tags:
- mathematics
- competition-math
- proof-evaluation
- llm-as-a-judge
- pairwise-comparison
- qualitative-analysis
size_categories:
- n<1K
viewer: false
---

# ProofRank: Qualitative Examples of Grading Disagreements

Companion artifact to the ICLR 2027 submission **"Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness"**.

We include supplementary examples in [`examples.md`](https://huggingface.co/datasets/Anon539823983/ProofRank-Examples/blob/main/EXAMPLES.md). Each one contains the problem ID and statement, two complete model-written solutions, and a short commentary explaining the nature of the disagreement.

## Contents

| # | Dimension | Problem | Solutions compared | What it illustrates |
|---|-----------|---------|--------------------|---------------------|
| 1 | Conciseness (human-human disagreement) | `imo-bench_number_theory-042` | GLM-5 vs. Gemini-3.1-Pro | Two solutions that are verbose in *different* ways, one padded with local restatements throughout, the other prefaced by a long recap of elementary facts, making the "more concise" call ambiguous. |
| 2 | Cognitive ease (human–human disagreement) | `shortlist_2025_6` | GLM-5 vs. GPT-5.4 | A rigorous, notation-heavy combinatorial argument vs. a more abstract counting argument requiring internal visualizatio, which reads as "easier" depends on the annotator's background. |
| 3 | Computational complexity (human–human disagreement) | `imo-bench_combinatorics-011` | Gemini-3-Flash vs. GPT-5.4 | Sparser notation whose individual claims are slower to verify vs. more symbols and algebraic steps that are each simple to parse. |
| 4 | LLM judge vs. human consensus | `aime_2025_27` | Qwen-3.5-397B vs. GPT-5.4 | Two near-identical solutions that both human annotators graded as a tie, while the LLM judge (GPT-OSS-120B) declared one more computationally complex. |

## Licensing

The problems are drawn from publicly available mathematics competitions and previously released benchmarks, and the human-written reference solutions are collected from public Art of Problem Solving posts and official competition materials. We abide by the sources' terms and conditions and redistribute this material under [**CC BY-NC-SA 4.0**](https://creativecommons.org/licenses/by-nc-sa/4.0/) - see [`LICENSE`](LICENSE) - for non-commercial research use and with proper credit to the original competitions.

The terms of the original sources continue to apply to the redistributed text, independently of that license:

- **Art of Problem Solving**: the forum content is **not available for model training** and remains subject to the applicable AoPS restrictions, which require attribution when the material is used as input to an AI system.
- **Official competition problems and previously released benchmarks**: typically in the public domain or released under comparable conditions, which likewise forbid use of the material for training.

Accordingly, this data **must not be used to train any AI model**. Users are responsible for complying with the original terms that apply to each entry.

Work produced by us - code, results, and evaluation scripts - is published under the more permissive **MIT** license.