---
title: "MUSTARD — paper by Huang et al. (2024) — summary and ideas"
description: "Training LLMs for mathematical reasoning and theorem proving requires step-by-step solutions, but… 44 references, cited by 29 papers here."
authors: ["Yinya Huang", "Xiaohan Lin", "Zhengying Liu", "Qingxing Cao", "Huajian Xin", "Haiming Wang", "Zhenguo Li", "Linqi Song", "Xiaodan Liang"]
year: 2024
venue: "arXiv:2402.08957 (ICLR 2024 spotlight)"
source: "https://arxiv.org/abs/2402.08957"
doi: "10.48550/arxiv.2402.08957"
arxiv: "2402.08957"
licence: "arXiv — non-exclusive licence to distribute"
licence_url: "https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/huang-2024-mustard-mastering-uniform-synthesis-theorem/"
---
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# MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data

**Authors:** [Yinya Huang](https://md.research.elamur.ai/free/en/authors/yinya-huang/), [Xiaohan Lin](https://md.research.elamur.ai/free/en/authors/xiaohan-lin/), [Zhengying Liu](https://md.research.elamur.ai/free/en/authors/zhengying-liu/), [Qingxing Cao](https://md.research.elamur.ai/free/en/authors/qingxing-cao/), [Huajian Xin](https://md.research.elamur.ai/free/en/authors/huajian-xin/), [Haiming Wang](https://md.research.elamur.ai/free/en/authors/haiming-wang/), [Zhenguo Li](https://md.research.elamur.ai/free/en/authors/zhenguo-li/), [Linqi Song](https://md.research.elamur.ai/free/en/authors/linqi-song/) and [Xiaodan Liang](https://md.research.elamur.ai/free/en/authors/xiaodan-liang/) · **Year:** 2024 · **Venue:** arXiv:2402.08957 (ICLR 2024 spotlight) · **Licence:** [arXiv — non-exclusive licence to distribute](https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html)

**Links:** [Publisher's page](https://arxiv.org/abs/2402.08957) · [PDF](https://arxiv.org/pdf/2402.08957v3) · [DOI 10.48550/arxiv.2402.08957](https://doi.org/10.48550/arxiv.2402.08957) · [arXiv 2402.08957](https://arxiv.org/abs/2402.08957) · [OpenAlex](https://openalex.org/W4391871516)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · [29](https://md.research.elamur.ai/free/en/papers/huang-2024-mustard-mastering-uniform-synthesis-theorem/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Training LLMs for mathematical reasoning and theorem proving requires step-by-step solutions, but such annotations are hard to obtain. Expert-written sets like miniF2F are small. Rule-checked or rule-generated data (ROSCOE, INT) either lacks guaranteed correctness or contains proofs with little mathematical meaning. MUSTARD addresses this with a synthesis pipeline that pairs an LLM's fluency with a formal prover's strict checking.

The pipeline has three stages. First, it samples one or two seed concepts from a pool built from Khan Academy courses. Second, it asks GPT-4 to write a problem, an informal proof and a Lean 3 formalization. Third, Lean Prover checks the formal proof; failed attempts are sent back to the model with the error messages so it can revise them.

The output is MUSTARD SAUCE, a benchmark of 5,866 prover-verified items. The authors report that prover verdicts agree with human quality judgments. Fine-tuning Llama 2-7B on the data improves both theorem proving and math word problems. This makes the approach a scalable route to verified and diverse math training data.

## Key points
- **Three-stage pipeline:** concept seeding, then GPT-4 generation of problem, informal proof and Lean 3 proof, then validation in Lean Prover with error-guided revision.
- **Concept pool:** drawn from Khan Academy and spanning four educational levels (elementary, middle, high school, higher education), each with 5–9 domains. It covers both theorem-proving and word-problem question types.
- **MUSTARD SAUCE:** 5,866 verified data points. Each pairs a natural-language problem statement and its natural-language proof with a formal proof that passes Lean.
- **Fine-tuning gains for Llama 2-7B:**
  - 15.41% average relative improvement in automated theorem proving
  - 8.18% average relative improvement on math word problems
  - +20.9% on zero-shot GSM8K
  - 8.7 pass@1 on mathlib
- **Availability:** code and data are released at github.com/Eleanor-H/MUSTARD (ICLR 2024 spotlight).

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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- [City University of Hong Kong](https://md.research.elamur.ai/free/en/universities/city-university-of-hong-kong/) — University, Hong Kong, China · 62 works · 3,563 citations

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## Cite

Cite as: Yinya Huang, Xiaohan Lin, Zhengying Liu, Qingxing Cao, Huajian Xin, Haiming Wang, Zhenguo Li, Linqi Song and Xiaodan Liang. 2024. MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data. arXiv:2402.08957 (ICLR 2024 spotlight).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{huang2024mustard,
  title = {{MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data}},
  author = {Yinya Huang, Xiaohan Lin, Zhengying Liu, Qingxing Cao, Huajian Xin, Haiming Wang, Zhenguo Li, Linqi Song and Xiaodan Liang},
  year = {2024},
  doi = {10.48550/arxiv.2402.08957},
  eprint = {2402.08957},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2402.08957}
}
```

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## References

44 references, 32 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter,… — [Language Models are Few-Shot Learners](https://md.research.elamur.ai/free/en/papers/brown-2020-language-models-few-shot-learners/)
2. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. [Training verifiers to solve math word problems](https://md.research.elamur.ai/free/en/papers/cobbe-2021-training-verifiers-solve-math-word/). CoRR, abs/2110.14168, 2021.
3. Leonardo Mendonça de Moura, Soonho Kong, Jeremy Avigad, Floris van Doorn, and Jakob von Raumer. The lean theorem prover (system description). In Amy P. Felty and Aart Middeldorp (eds.), Automated Deduction - CADE-25 - 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7… [find](https://scholar.google.com/scholar?q=Leonardo+Mendonc%CC%A7a+de+Moura%2C+Soonho+Kong%2C+Jeremy+Avigad%2C+Floris+van+Doorn%2C+and+Jakob+von+Raumer%2E+The+lean+theorem+prover+%28system+description%29%2E+In+Amy+P%2E+Felty+and+Aart+Middeldorp+%28eds%2E%29%2C+Automated+Ded)
4. Springer, 2015. doi: 10.1007/978-3-319-21401-6\\ 26. URL https://doi.org/10.1007/978-3-319-21401-6_26. — [doi:10.1007/978-3-319-21401-6\](https://doi.org/10.1007/978-3-319-21401-6\) [↗](https://doi.org/10.1007/978-3-319-21401-6_26)
5. Olga Golovneva, Moya Chen, Spencer Poff, Martin Corredor, Luke Zettlemoyer, Maryam Fazel-Zarandi, and Asli Celikyilmaz. [ROSCOE: A suite of metrics for scoring step-by-step reasoning](https://md.research.elamur.ai/free/en/papers/golovneva-2022-roscoe-suite-metrics-scoring-step/). In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023.
6. OpenReview.net, 2023. URL [https://openreview.net/pdf?id=xYlJRpzZtsY](https://openreview.net/pdf?id=xYlJRpzZtsY). [↗](https://openreview.net/pdf?id=xYlJRpzZtsY)
7. Jesse Michael Han, Jason Rute, Yuhuai Wu, Edward W. Ayers, and Stanislas Polu. [Proof artifact co-training for theorem proving with language models](https://md.research.elamur.ai/free/en/papers/han-2021-proof-artifact-co-training-theorem/). In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022.
8. OpenReview.net, 2022. URL [https://openreview.net/forum?id=rpxJc9j04U](https://openreview.net/forum?id=rpxJc9j04U). [↗](https://openreview.net/forum?id=rpxJc9j04U)
9. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. [Measuring mathematical problem solving with the MATH dataset](https://md.research.elamur.ai/free/en/papers/hendrycks-2021-measuring-mathematical-problem-solving-math/). In Joaquin Vanschoren and Sai-Kit Yeung (eds.), Proceedings of the Neural Information Processing Systems Track on Dataset…
10. Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. [Lora: Low-rank adaptation of large language models](https://md.research.elamur.ai/free/en/papers/hu-2021-lora-low-rank-adaptation-large/). arXiv preprint arXiv:2106.09685, 2021.
11. Albert Qiaochu Jiang, Sean Welleck, Jin Peng Zhou, Timothée Lacroix, Jiacheng Liu, Wenda Li, Mateja Jamnik, Guillaume Lample, and Yuhuai Wu. [Draft, sketch, and prove: Guiding formal theorem provers with informal proofs](https://md.research.elamur.ai/free/en/papers/jiang-2022-draft-sketch-prove-guiding-formal/). In The Eleventh International Conference on Learning Representations, ICLR 2023…
12. OpenReview.net, 2023. URL [https://openreview.net/pdf?id=SMa9EAovKMC](https://openreview.net/pdf?id=SMa9EAovKMC). [↗](https://openreview.net/pdf?id=SMa9EAovKMC)
13. Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yutaka Matsuo, and Yusuke Iwasawa. [Large language models are zero-shot reasoners](https://md.research.elamur.ai/free/en/papers/kojima-2022-large-language-models-zero-shot/). In NeurIPS, 2022. URL [http://papers.nips.cc/paper_files/paper/2022/hash/8bb0d291acd4acf06ef112099c16f326-Abstract-Conference.html](http://papers.nips.cc/paper_files/paper/2022/hash/8bb0d291acd4acf06ef112099c16f326-Abstract-Conference.html). [↗](http://papers.nips.cc/paper_files/paper/2022/hash/8bb0d291acd4acf06ef112099c16f326-Abstract-Conference.html)
14. Xian Li, Ping Yu, Chunting Zhou, Timo Schick, Luke Zettlemoyer, Omer Levy, Jason Weston, and Mike Lewis. [Self-alignment with instruction backtranslation](https://md.research.elamur.ai/free/en/papers/li-2023-self-alignment-instruction-backtranslation/). CoRR, abs/2308.06259, 2023. doi: 10.48550/arXiv.2308.06259. URL https://doi.org/10.48550/arXiv.2308.06259. [↗](https://doi.org/10.48550/arXiv.2308.06259)
15. Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. arXiv preprint arXiv:2305.[20050, 2023](https://md.research.elamur.ai/free/en/papers/lightman-2023-let-s-verify-step-step/).
16. Chin-Yew Lin. [ROUGE: A package for automatic evaluation of summaries](https://md.research.elamur.ai/free/en/papers/lin-2004-rouge-package-automatic-evaluation-summaries/). In Text Summarization Branches Out, pp. 74–81, Barcelona, Spain, July 2004. Association for Computational Linguistics. URL https://aclanthology.org/W04-1013. [↗](https://aclanthology.org/W04-1013)
17. Chengwu Liu, Jianhao Shen, Huajian Xin, Zhengying Liu, Ye Yuan, Haiming Wang, Wei Ju, Chuanyang Zheng, Yichun Yin, Lin Li, Ming Zhang, and Qun Liu. [FIMO: A challenge formal dataset for automated theorem proving](https://md.research.elamur.ai/free/en/papers/liu-2023-fimo-challenge-formal-dataset-automated/). CoRR, abs/2309.04295, 2023.
18. OpenAI. Introducing chatgpt, 2022. [find](https://scholar.google.com/scholar?q=OpenAI%2E+Introducing+chatgpt%2C+2022%2E)
19. OpenAI. [GPT-4 technical report](https://md.research.elamur.ai/free/en/papers/openai-2023-gpt-4-technical-report/). CoRR, abs/2303.08774, 2023.
20. Stanislas Polu and Ilya Sutskever. [Generative language modeling for automated theorem proving](https://md.research.elamur.ai/free/en/papers/polu-2020-generative-language-modeling-automated-theorem/). CoRR, abs/2009.03393, 2020. URL https://arxiv.org/abs/2009.03393. [↗](https://arxiv.org/abs/2009.03393)
21. Stanislas Polu, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Igor Babuschkin, and Ilya Sutskever. [Formal mathematics statement curriculum learning](https://md.research.elamur.ai/free/en/papers/polu-2022-formal-mathematics-statement-curriculum-learning/). In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023.
22. OpenReview.net, 2023. URL [https://openreview.net/pdf?id=-P7G-8dmSh4](https://openreview.net/pdf?id=-P7G-8dmSh4). [↗](https://openreview.net/pdf?id=-P7G-8dmSh4)
23. Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, Ilya Sutskever, et al. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019. [find](https://scholar.google.com/scholar?q=Alec+Radford%2C+Jeffrey+Wu%2C+Rewon+Child%2C+David+Luan%2C+Dario+Amodei%2C+Ilya+Sutskever%2C+et+al%2E+Language+models+are+unsupervised+multitask+learners%2E+OpenAI+blog%2C+1%288%29%3A9%2C+2019%2E)
24. Abulhair Saparov and He He. [Language models are greedy reasoners: A systematic formal analysis of chain-of-thought](https://md.research.elamur.ai/free/en/papers/saparov-2022-language-models-greedy-reasoners-systematic/). In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023.
25. Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, Dan Bikel, Lukas Blecher, Cristian Canton-Ferrer, Moya Chen, Guillem Cucurull, David Esiobu, Jude Fernandes, Jeremy Fu, Wenyin Fu, Brian Fuller,… — [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://md.research.elamur.ai/free/en/papers/touvron-2023-llama-2-open-foundation-fine/)
26. Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. [Attention is all you need](https://md.research.elamur.ai/free/en/papers/vaswani-2017-attention-all-need/). Advances in neural information processing systems, 30, 2017.
27. Haiming Wang, Ye Yuan, Zhengying Liu, Jianhao Shen, Yichun Yin, Jing Xiong, Enze Xie, Han Shi, Yujun Li, Lin Li, Jian Yin, Zhenguo Li, and Xiaodan Liang. [Dt-solver: Automated theorem proving with dynamic-tree sampling guided by proof-level value function](https://md.research.elamur.ai/free/en/papers/wang-2023-dt-solver-automated-theorem-proving/). In Anna Rogers, Jordan L. Boyd-Graber, and N…
28. Haiming Wang, Huajian Xin, Chuanyang Zheng, Zhengying Liu, Qingxing Cao, Yinya Huang, Jing Xiong, Han Shi, Enze Xie, Jian Yin, Zhenguo Li, and Xiaodan Liang. [LEGO-prover: Neural theorem proving with growing libraries](https://md.research.elamur.ai/free/en/papers/wang-2023-lego-prover-neural-theorem-proving/). In The Twelfth International Conference on Learning Representations, 2024. URL htt…
29. Mingzhe Wang and Jia Deng. [Learning to prove theorems by learning to generate theorems](https://md.research.elamur.ai/free/en/papers/wang-2020-learning-prove-theorems-learning-generate/). In Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.), Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Sy…
30. Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc V. Le, Ed H. Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. [Self-consistency improves chain of thought reasoning in language models](https://md.research.elamur.ai/free/en/papers/wang-2022-self-consistency-improves-chain-thought/). In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023.
31. OpenReview.net, 2023b. URL [https://openreview.net/pdf?id=1PL1NIMMrw](https://openreview.net/pdf?id=1PL1NIMMrw). [↗](https://openreview.net/pdf?id=1PL1NIMMrw)
32. Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A. Smith, Daniel Khashabi, and Hannaneh Hajishirzi. Self-instruct: Aligning language models with self-generated instructions. In Anna Rogers, Jordan L. Boyd-Graber, and Naoaki Okazaki (eds.), Proceedings of the 61st Annual Meeting of the A… [find](https://scholar.google.com/scholar?q=Yizhong+Wang%2C+Yeganeh+Kordi%2C+Swaroop+Mishra%2C+Alisa+Liu%2C+Noah+A%2E+Smith%2C+Daniel+Khashabi%2C+and+Hannaneh+Hajishirzi%2E+Self%2Dinstruct%3A+Aligning+language+models+with+self%2Dgenerated+instructions%2E+In+Anna+Roger)
33. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed H. Chi, Quoc V. Le, and Denny Zhou. [Chain-of-thought prompting elicits reasoning in large language models](https://md.research.elamur.ai/free/en/papers/wei-2022-chain-thought-prompting-elicits-reasoning/). In NeurIPS, 2022. URL [http://papers.nips.cc/paper_files/paper/2022/hash/9d5609613524ecf4f15af0f7b31abca4-Abstra…](http://papers.nips.cc/paper_files/paper/2022/hash/9d5609613524ecf4f15af0f7b31abca4-Abstra…) [↗](http://papers.nips.cc/paper_files/paper/2022/hash/9d5609613524ecf4f15af0f7b31abca4-Abstra…)
34. Peter West, Chandra Bhagavatula, Jack Hessel, Jena D. Hwang, Liwei Jiang, Ronan Le Bras, Ximing Lu, Sean Welleck, and Yejin Choi. [Symbolic knowledge distillation: from general language models to commonsense models](https://md.research.elamur.ai/free/en/papers/west-2022-symbolic-knowledge-distillation-general-language/). In Marine Carpuat, Marie-Catherine de Marneffe, and Iván Vladimir Meza Ruı́z (eds.),…
35. Yuhuai Wu, Albert Q. Jiang, Jimmy Ba, and Roger Baker Grosse. [INT: an inequality benchmark for evaluating generalization in theorem proving](https://md.research.elamur.ai/free/en/papers/wu-2020-int-inequality-benchmark-evaluating-generalization/). In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021.
36. OpenReview.net, 2021. URL [https://openreview.net/forum?id=O6LPudowNQm](https://openreview.net/forum?id=O6LPudowNQm). [↗](https://openreview.net/forum?id=O6LPudowNQm)
37. Yuhuai Wu, Albert Qiaochu Jiang, Wenda Li, Markus N. Rabe, Charles Staats, Mateja Jamnik, and Christian Szegedy. [Autoformalization with large language models](https://md.research.elamur.ai/free/en/papers/wu-2022-autoformalization-large-language-models/). In NeurIPS, 2022. URL [http://papers.nips.cc/paper_files/paper/2022/hash/d0c6bc641a56bebee9d985b937307367-Abstract-Conference.html](http://papers.nips.cc/paper_files/paper/2022/hash/d0c6bc641a56bebee9d985b937307367-Abstract-Conference.html). [↗](http://papers.nips.cc/paper_files/paper/2022/hash/d0c6bc641a56bebee9d985b937307367-Abstract-Conference.html)
38. Jing Xiong, Jianhao Shen, Ye Yuan, Haiming Wang, Yichun Yin, Zhengying Liu, Lin Li, Zhijiang Guo, Qingxing Cao, Yinya Huang, Chuanyang Zheng, Xiaodan Liang, Ming Zhang, and Qun Liu. [TRIGO: Benchmarking formal mathematical proof reduction for generative language models](https://md.research.elamur.ai/free/en/papers/xiong-2023-trigo-benchmarking-formal-mathematical-proof/). In Houda Bouamor, Juan Pino, a…
39. Jing Xiong, Zixuan Li, Chuanyang Zheng, Zhijiang Guo, Yichun Yin, Enze Xie, Zhicheng YANG, Qingxing Cao, Haiming Wang, Xiongwei Han, Jing Tang, Chengming Li, and Xiaodan Liang. [DQ-lore: Dual queries with low rank approximation re-ranking for in-context learning](https://md.research.elamur.ai/free/en/papers/xiong-2023-dq-lore-dual-queries-low/). In The Twelfth International Conferen…
40. Can Xu, Qingfeng Sun, Kai Zheng, Xiubo Geng, Pu Zhao, Jiazhan Feng, Chongyang Tao, and Daxin Jiang. Wizardlm: Empowering large language models to follow complex instructions. CoRR, abs/2304.[12244, 2023](https://md.research.elamur.ai/free/en/papers/xu-2023-wizardlm-empowering-large-pre-trained/). doi: 10.48550/arXiv.2304.12244. URL https://doi.org/10.48550/arXiv.2304.12244. [↗](https://doi.org/10.48550/arXiv.2304.12244)
41. Siyu Yuan, Jiangjie Chen, Ziquan Fu, Xuyang Ge, Soham Shah, Charles Robert Jankowski, Yanghua Xiao, and Deqing Yang. Distilling script knowledge from large language models for constrained language planning. In Anna Rogers, Jordan L. Boyd-Graber, and Naoaki Okazaki (eds.), Proceedings of the 61st Ann… [find](https://scholar.google.com/scholar?q=Siyu+Yuan%2C+Jiangjie+Chen%2C+Ziquan+Fu%2C+Xuyang+Ge%2C+Soham+Shah%2C+Charles+Robert+Jankowski%2C+Yanghua+Xiao%2C+and+Deqing+Yang%2E+Distilling+script+knowledge+from+large+language+models+for+constrained+language+pla)
42. Chuanyang Zheng, Zhengying Liu, Enze Xie, Zhenguo Li, and Yu Li. [Progressive-hint prompting improves reasoning in large language models](https://md.research.elamur.ai/free/en/papers/zheng-2023-progressive-hint-prompting-improves-reasoning/). arXiv preprint arXiv:2304.09797, 2023a.
43. Chuanyang Zheng, Haiming Wang, Enze Xie, Zhengying Liu, Jiankai Sun, Huajian Xin, Jianhao Shen, Zhenguo Li, and Yu Li. [Lyra: Orchestrating dual correction in automated theorem proving](https://md.research.elamur.ai/free/en/papers/zheng-2023-lyra-orchestrating-dual-correction-automated/). arXiv preprint arXiv:2309.15806, 2023b.
44. Kunhao Zheng, Jesse Michael Han, and Stanislas Polu. [minif2f: a cross-system benchmark for formal olympiad-level mathematics](https://md.research.elamur.ai/free/en/papers/zheng-2021-minif2f-cross-system-benchmark-formal/). In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022.

*Updated 3 November 2026*