Anon539823983/ProofRank-Examples

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. 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 - 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:

• 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.