ProofRank: Evaluating LLM Proof Quality Beyond Correctness
Collection
NeurIPS 2026 (E&D). Code: github.com/insait-institute/proofrank • 4 items • Updated
example_id stringclasses 8
values | group stringclasses 2
values | title stringclasses 8
values | problem_id stringclasses 6
values | solution_1_model stringclasses 6
values | solution_2_model stringclasses 6
values | content_markdown stringclasses 8
values |
|---|---|---|---|---|---|---|
contentious_1 | contentious | Ex. 1: Conciseness disagreement | imo-bench_number_theory-042 | GLM-5 | Gemini-3.1-Pro | # Ex. 1: Conciseness disagreement
**Problem** `imo-bench_number_theory-042`
> **Problem statement:** Find all positive integers $k$ such that the number of positive divisors of $2k^3$ is $2k$.
**Solution 1 (GLM-5)**
We are to find all positive integers \(k\) such that the number of positive divisors of \(2k^3\) equ... |
contentious_2 | contentious | Ex. 2: Human disagreement on Cognitive Ease | shortlist_2025_6 | GLM-5 | GPT-5.4 | # Ex. 2: Human disagreement on Cognitive Ease
**Problem**: `shortlist_2025_6`
**Problem Statement**: Jerry places at most one rook in each cell of a $2025 \times 2025$ grid of cells. A rook attacks another rook if the two rooks are in the same row or column and there are no other rooks between them. Determine the maxi... |
contentious_3 | contentious | Ex. 3: Human disagreement on Computational Complexity | imo-bench_combinatorics-011 | Gemini-3-Flash | GPT-5.4 | # Ex. 3: Human disagreement on Computational Complexity
**Problem:** `imo-bench_combinatorics-011`
**Problem statement:** A soccer player named Ronaldo stands on a point on a circle with circumference $1$. Given an infinite sequence of positive real numbers $c_1, c_2, c_3, \dots$, Ronaldo successively runs distances $... |
contentious_4 | contentious | Ex. 4: GPT-OSS-120B disagrees with human judges on pairwise comparisons | aime_2025_27 | Qwen-3.5-397B | GPT-5.4 | # Ex. 4: GPT-OSS-120B disagrees with human judges on pairwise comparisons
**Problem:** `aime_2025_27`
**Problem statement:** Let $A_1 A_2 A_3 \ldots A_{11}$ be an $11$-sided non-convex simple polygon with the following properties:
\begin{itemize}
\item For every integer $2 \le i \le 10$, the area of $\triangle A_i ... |
clear_cut_1 | clear_cut | E1. `aime_2025_27`: verbosity separates, all other constructs untouched | aime_2025_27 | gemini/gemini-3-flash | gemini/gemini-31-pro | # E1. `aime_2025_27`: verbosity separates, all other constructs untouched
**Problem:**
> Let $A_1 A_2 A_3 \ldots A_{11}$ be an $11$-sided non-convex simple polygon with the following properties:
>
> - For every integer $2 \le i \le 10$, the area of $\triangle A_i A_{1} A_{i+1}$ is equal to $1$.
> - For every integer ... |
clear_cut_2 | clear_cut | E2. `shortlist_2025_6`: full agreement, all verdicts decisive | shortlist_2025_6 | gemini/gemini-3-flash | stepfun/3.5-flash | # E2. `shortlist_2025_6`: full agreement, all verdicts decisive
**Problem:**
> Jerry places at most one rook in each cell of a $2025 \times 2025$ grid of cells. A rook attacks another rook if the two rooks are in the same row or column and there are no other rooks between them. Determine the maximum number of rooks J... |
clear_cut_3 | clear_cut | E3. `imo-bench_geometry-013`: full agreement, decisive verdicts plus agreed ties | imo-bench_geometry-013 | glm/glm-5 | qwen/qwen35_397b_a17b_high | # E3. `imo-bench_geometry-013`: full agreement, decisive verdicts plus agreed ties
**Problem:**
> In triangle $XYZ$, we have $XY = YZ$, $\angle Y = 20^\circ$. Point $P$ on $XZ$ is such that $XP : PZ = 1 : 2$, point $Q$ is the projection of $Z$ to $YP$. Find angle $\angle XQY$ in terms of degree.
**Annotator verdicts... |
clear_cut_4 | clear_cut | E4. `aime_2026_9`: fewer words, unanimously more verbose | aime_2026_9 | qwen/qwen35_397b_a17b_high | openai/gpt-54 | # E4. `aime_2026_9`: fewer words, unanimously more verbose
**Problem** (middle portion truncated in the source dossier; paste the full statement before sharing):
> Joanne has a blank fair six-sided die and six stickers each displaying a different integer from 1 to 6. Joanne rolls the die and then places the sticker l... |
ProofRank: Annotated Pairwise Comparison Examples
We include eight pairs of LLM-written solutions from the human annotation study of ProofRank, each with the problem, both solutions, the annotators' verdicts, and a commentary for the case studies given in the paper:
clear_cut_1--clear_cut_4: pairs on which both annotators independently reached the same verdicts.contentious_1--contentious_4: pairs on which the annotators split, or on which the LLM judge (GPT-OSS-120B) disagreed with them.
Files
| File | Content |
|---|---|
data/examples.jsonl |
One row per example (fields below); this is the machine-readable version. |
examples_agreement.md |
The four clear-cut examples, rendered as markdown. |
EXAMPLES.md |
The four contentious examples, rendered as markdown. |
| Column | Type | Description |
|---|---|---|
example_id |
string | clear_cut_<n> or contentious_<n>. |
group |
string | clear_cut or contentious. |
title |
string | Short description of what the example illustrates. |
problem_id |
string | Problem identifier in ProofRank. |
solution_1_model, solution_2_model |
string | Models that wrote the two solutions. |
content_markdown |
string | Problem, both solutions, annotator verdicts and commentary, as markdown. |
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 - see 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. Namely, for official competition problems and previously released benchmarks, they 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.
Citation
@inproceedings{petrov2026proofrank,
title={Not All Proofs Are Equal: Evaluating {LLM} Proof Quality Beyond Correctness},
author={Petrov, Ivo and Dekoninck, Jasper and Dimitrov, Dimitar I. and Vechev, Martin},
booktitle={The Fortieth Annual Conference on Neural Information Processing Systems Evaluations and Datasets Track},
year={2026},
url={https://openreview.net/forum?id=Zf9xKiTAom}
}
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