The paper introduces SymCE, a dataset of 4,707 false undergraduate‑algebra and real‑analysis conjectures each paired with a deterministic Python verifier that can be executed to check truth. It studies counterexample generation by training a 4B‑parameter language model (Qwen3‑4B) first with supervised fine‑tuning and then with reinforcement learning (GRPO) using the verifier as a reward. The results show that counterexample‑only fine‑tuning can destroy true‑theorem recognition, while reinforcement learning with a sparse outcome‑only reward restores and surpasses baseline performance, achieving higher success rates than larger open‑weight models and competitive performance on other math benchmarks.
"whyItMatters":"The study demonstrates that reinforcement learning guided by a per‑theorem verifier can effectively repair the shortcomings of supervised fine‑tuning in theorem proving, offering a practical approach to improve language models’ mathematical reasoning capabilities."
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