record stringlengths 1.12k 1.72M |
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{"problem_id": "aime_2026_28", "problem": "Call finite sets of integers $S$ and $T$ cousins if\n- $S$ and $T$ have the same number of elements,\n- $S$ and $T$ are disjoint, and\n- the elements of $S$ can be paired with the elements of $T$ so that the elements in each pair differ by exactly $1$.\nFor example, $\\{1,2,5\... |
{"problem_id": "aime_2026_28-part1", "problem": "Call finite sets of integers $S$ and $T$ cousins if\n- $S$ and $T$ have the same number of elements,\n- $S$ and $T$ are disjoint, and\n- the elements of $S$ can be paired with the elements of $T$ so that the elements in each pair differ by exactly $1$.\nFor example, $\\{... |
{"problem_id": "hmmt_feb_2026_26", "problem": "Let \\(ABC\\) be a triangle, and \\(M\\) be the midpoint of segment \\(\\overline{BC}\\). Points \\(P\\) and \\(Q\\) lie on segments \\(\\overline{AB}\\) and \\(\\overline{AC}\\), respectively, so that \\(\\angle PMB = \\angle QMC = \\frac{1}{2}\\angle BAC\\). Given that \... |
{"problem_id": "hmmt_feb_2026_26-part1", "problem": "Let \\(ABC\\) be a triangle, and \\(M\\) be the midpoint of segment \\(\\overline{BC}\\). Points \\(P\\) and \\(Q\\) lie on segments \\(\\overline{AB}\\) and \\(\\overline{AC}\\), respectively, so that \\(\\angle PMB = \\angle QMC = \\frac{1}{2}\\angle BAC\\). Given ... |
{"problem_id": "hmmt_feb_2026_26-part2", "problem": "Let \\(ABC\\) be a triangle, and \\(M\\) be the midpoint of segment \\(\\overline{BC}\\). Points \\(P\\) and \\(Q\\) lie on segments \\(\\overline{AB}\\) and \\(\\overline{AC}\\), respectively, so that \\(\\angle PMB = \\angle QMC = \\frac{1}{2}\\angle BAC\\). Given ... |
{"problem_id": "hmmt_feb_2026_26-part3", "problem": "Let \\(ABC\\) be a triangle, and \\(M\\) be the midpoint of segment \\(\\overline{BC}\\). Points \\(P\\) and \\(Q\\) lie on segments \\(\\overline{AB}\\) and \\(\\overline{AC}\\), respectively, so that \\(\\angle PMB = \\angle QMC = \\frac{1}{2}\\angle BAC\\). Given ... |
{"problem_id": "hmmt_feb_2026_26-part4", "problem": "Let \\(ABC\\) be a triangle, and \\(M\\) be the midpoint of segment \\(\\overline{BC}\\). Points \\(P\\) and \\(Q\\) lie on segments \\(\\overline{AB}\\) and \\(\\overline{AC}\\), respectively, so that \\(\\angle PMB = \\angle QMC = \\frac{1}{2}\\angle BAC\\). Given ... |
{"problem_id": "hmmt_feb_2026_16", "problem": "Derek currently owes $\\pi$ units of a currency called Money of Indiscrete Type, or MIT for short. Every day, the following happens:\n\n- He flips a fair coin to decide how much of his debt to pay. If he flips heads, he decreases his debt by 1 MIT. If he flips tails, he de... |
{"problem_id": "hmmt_feb_2026_16-part1", "problem": "Derek currently owes $\\pi$ units of a currency called Money of Indiscrete Type, or MIT for short. Every day, the following happens:\n\n- He flips a fair coin to decide how much of his debt to pay. If he flips heads, he decreases his debt by 1 MIT. If he flips tails,... |
{"problem_id": "hmmt_feb_2026_16-part2", "problem": "Derek currently owes $\\pi$ units of a currency called Money of Indiscrete Type, or MIT for short. Every day, the following happens:\n\n- He flips a fair coin to decide how much of his debt to pay. If he flips heads, he decreases his debt by 1 MIT. If he flips tails,... |
{"problem_id": "hmmt_feb_2026_25", "problem": "Three circles of radius 2 are internally tangent to a circle $\\Omega$ centered at $O$ of radius 11, and three chords of $\\Omega$ are each tangent to two of the three circles. Given that $O$ lies inside the triangle formed by the three chords and two of the chords have le... |
{"problem_id": "hmmt_feb_2026_25-part1", "problem": "Three circles of radius 2 are internally tangent to a circle $\\Omega$ centered at $O$ of radius 11, and three chords of $\\Omega$ are each tangent to two of the three circles. Given that $O$ lies inside the triangle formed by the three chords and two of the chords h... |
{"problem_id": "hmmt_feb_2026_14", "problem": "Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes.", "original_problem"... |
{"problem_id": "hmmt_feb_2026_14-part1", "problem": "Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes.", "original_pr... |
{"problem_id": "hmmt_feb_2026_14-part2", "problem": "Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes.", "original_pr... |
{"problem_id": "hmmt_feb_2026_14-part3", "problem": "Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes.", "original_pr... |
{"problem_id": "hmmt_feb_2026_14-part4", "problem": "Sarunyu has a stick of length 1 with one endpoint marked in red. Every minute, he picks one of his sticks uniformly at random and breaks it into two halves of equal length. Compute the expected length of the stick with the red endpoint after 5 minutes.", "original_pr... |
{"problem_id": "hmmt_feb_2026_20", "problem": "Let \\(S\\) be the set of all ordered pairs \\((x, y)\\) of nonnegative integers \\(0 \\leq x \\leq 19\\) and \\(0 \\leq y \\leq 2\\). Compute the number of permutations \\((x_1, y_1)\\), \\((x_2, y_2)\\), ..., \\((x_{60}, y_{60})\\) of the elements of \\(S\\) such that\n\... |
{"problem_id": "hmmt_feb_2026_5", "problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloor)!^{n!} + 450.\n\\]", "original_problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloor)!^{n... |
{"problem_id": "hmmt_feb_2026_5-part1", "problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloor)!^{n!} + 450.\n\\]", "original_problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloo... |
{"problem_id": "hmmt_feb_2026_5-part2", "problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloor)!^{n!} + 450.\n\\]", "original_problem": "Compute the largest positive integer \\( n \\) such that\n\n\\[\nn \\text{ divides } (\\lfloor \\sqrt{n} \\rfloo... |
{"problem_id": "hmmt_feb_2026_9", "problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{-\\lfloor 101k/2 \\rfloor} + \\cdots + 2^{-\\lfloor 101k/100 \\rfloor} \\right). \\]", "original_problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{-\\lfl... |
{"problem_id": "hmmt_feb_2026_9-part1", "problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{-\\lfloor 101k/2 \\rfloor} + \\cdots + 2^{-\\lfloor 101k/100 \\rfloor} \\right). \\]", "original_problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{... |
{"problem_id": "hmmt_feb_2026_9-part2", "problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{-\\lfloor 101k/2 \\rfloor} + \\cdots + 2^{-\\lfloor 101k/100 \\rfloor} \\right). \\]", "original_problem": "Compute\n\n\\[ \\sum_{k=1}^{\\infty} \\left( 2^{-\\lfloor 101k/1 \\rfloor} + 2^{... |
{"problem_id": "hmmt_feb_2026_15", "problem": "Let $S$ be the set of positive integer divisors of $10^9$. Compute the number of subsets $T$ of $S$ such that\n\n- for every element $s$ of $S$, exactly one of $s$ and $10^9/s$ is in $T$, and\n- for every element $t$ of $T$, all positive integer divisors of $t$ are in $T$.... |
{"problem_id": "hmmt_feb_2026_15-part1", "problem": "Let $S$ be the set of positive integer divisors of $10^9$. Compute the number of subsets $T$ of $S$ such that\n\n- for every element $s$ of $S$, exactly one of $s$ and $10^9/s$ is in $T$, and\n- for every element $t$ of $T$, all positive integer divisors of $t$ are i... |
{"problem_id": "hmmt_feb_2026_15-part2", "problem": "Let $S$ be the set of positive integer divisors of $10^9$. Compute the number of subsets $T$ of $S$ such that\n\n- for every element $s$ of $S$, exactly one of $s$ and $10^9/s$ is in $T$, and\n- for every element $t$ of $T$, all positive integer divisors of $t$ are i... |
{"problem_id": "hmmt_feb_2026_27", "problem": "Let \\( ABC \\) be an isosceles triangle with \\( AB = AC \\). Points \\( P \\) and \\( Q \\) are located inside triangle \\( ABC \\) such that \\( BP = PQ = QC \\). Suppose that \\( \\angle BAP = 20^\\circ \\), \\( \\angle PAQ = 46^\\circ \\), and \\( \\angle QAC = 26^\\c... |
{"problem_id": "hmmt_feb_2026_27-part1", "problem": "Let \\( ABC \\) be an isosceles triangle with \\( AB = AC \\). Points \\( P \\) and \\( Q \\) are located inside triangle \\( ABC \\) such that \\( BP = PQ = QC \\). Suppose that \\( \\angle BAP = 20^\\circ \\), \\( \\angle PAQ = 46^\\circ \\), and \\( \\angle QAC = ... |
{"problem_id": "hmmt_feb_2026_27-part2", "problem": "Let \\( ABC \\) be an isosceles triangle with \\( AB = AC \\). Points \\( P \\) and \\( Q \\) are located inside triangle \\( ABC \\) such that \\( BP = PQ = QC \\). Suppose that \\( \\angle BAP = 20^\\circ \\), \\( \\angle PAQ = 46^\\circ \\), and \\( \\angle QAC = ... |
{"problem_id": "hmmt_feb_2026_27-part3", "problem": "Let \\( ABC \\) be an isosceles triangle with \\( AB = AC \\). Points \\( P \\) and \\( Q \\) are located inside triangle \\( ABC \\) such that \\( BP = PQ = QC \\). Suppose that \\( \\angle BAP = 20^\\circ \\), \\( \\angle PAQ = 46^\\circ \\), and \\( \\angle QAC = ... |
{"problem_id": "hmmt_feb_2026_27-part4", "problem": "Let \\( ABC \\) be an isosceles triangle with \\( AB = AC \\). Points \\( P \\) and \\( Q \\) are located inside triangle \\( ABC \\) such that \\( BP = PQ = QC \\). Suppose that \\( \\angle BAP = 20^\\circ \\), \\( \\angle PAQ = 46^\\circ \\), and \\( \\angle QAC = ... |
{"problem_id": "hmmt_feb_2026_31", "problem": "Jessica the jackrabbit wants to climb down a wall. The wall consists of 2026 horizontal layers stacked vertically. The $n$th layer from the top is partitioned into $2^n - 1$ identical rectangular bricks arranged side by side. Jessica begins in the topmost layer, which cont... |
{"problem_id": "hmmt_feb_2026_31-part1", "problem": "Jessica the jackrabbit wants to climb down a wall. The wall consists of 2026 horizontal layers stacked vertically. The $n$th layer from the top is partitioned into $2^n - 1$ identical rectangular bricks arranged side by side. Jessica begins in the topmost layer, whic... |
{"problem_id": "hmmt_feb_2026_31-part2", "problem": "Jessica the jackrabbit wants to climb down a wall. The wall consists of 2026 horizontal layers stacked vertically. The $n$th layer from the top is partitioned into $2^n - 1$ identical rectangular bricks arranged side by side. Jessica begins in the topmost layer, whic... |
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ProofRank: Evaluation Outputs
Companion artifact to the NeurIPS 2026 submission "Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness".
This dataset contains the complete LLM-judge outputs behind every number reported in the paper, so that all results can be recomputed without re-querying any model. It covers the ten evaluated models (GPT-5.4, Gemini-3.1-Pro, Gemini-3-Flash, GLM-5, DeepSeek-v3.2, Kimi-K2.5-Think, StepFun-3.5-Flash, Qwen3.5-397B, Grok-4.1-Fast, and GPT-OSS-120B) on the 382 benchmark problems, across all five proof-quality metrics (conciseness, computational ease, cognitive simplicity, diversity, and adaptivity) plus the correctness verification.
The benchmark problems themselves (with the human solution summaries and requested techniques) are released separately as the ProofRank dataset.
Contents
Each configuration of this repository is one evaluation artifact:
| Config(s) | Rows | Description |
|---|---|---|
answer_checker*, completeness_checker* |
~25k | Final-answer and completeness judgments (GPT-OSS-120B) for the main, diversity, adaptivity, and conciseness-prompting runs (Sec. 3.3) |
verbosity_rephrase, verbosity_rephrase_2/3 |
~6.5k | Rephraser outputs used for the compressibility-based conciseness metric, for the default and the two concise prompts (Sec. 3.2, 4.2) |
verbosity_verifier |
3,425 | Validity judgments of the rephrasings (App. C.2) |
technique_verifier |
4,406 | Judgments of whether a solution follows the requested technique (adaptivity, Sec. 3.2) |
summary_diversity_clustering_main, _with_human |
1,183 | Technique clusterings of the sampled solutions, without and with the human solutions (Sec. 3.2, 4.3) |
topic_classifier |
382 | Topic labels per problem |
pairwise_judgments |
~102k | Pairwise computational-ease / cognitive-simplicity verdicts, per evaluation setting (Sec. 3.2) |
pairwise_raw |
27,626 | The underlying raw pairwise judge files, needed to recompute the Bradley–Terry ratings from scratch |
correctness_raw |
600 | GPT-5.4 reference judgments and the corresponding checker judgments on the 200 sampled solutions used to validate the correctness filter (App. B.4) |
clustering_raw |
755 | Clusterings of the human solutions (and human + initial LLM solutions), used for diversity problem selection (Sec. 3.3) |
correctness_labels |
~15k | Derived per-solution correctness labels (informational; re-derived from the checker outputs during evaluation) |
diversity_samples, human_solutions, all_solutions, raw_problems |
~17.6k | The compiled solution samples and problem/solution data files consumed by the evaluation scripts |
Usage
Run the following command using the code file provided in this repository to regenerate the samples (pickled for caching, but full outputs can be restored):
python scripts/data/import_review_datasets.py --from-hub --repo-id Anon987281293/ProofRank-outputs --overwrite
License
This artifact is released under the Creative Commons Attribution-ShareAlike 4.0 International license, matching the license of the submission's main data release.
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