miniF2F-Lean Revisited: Reviewing Limitations and Charting a Path Forward

TL;DR

This paper revisits the miniF2F benchmark, analyzing the limitations of current AI systems in formal mathematical reasoning, and introduces miniF2F-v2 with improved accuracy and verified statements to better evaluate progress in the field.

Contribution

The paper provides a detailed analysis of miniF2F's limitations, corrects discrepancies to create miniF2F-v2, and demonstrates significant accuracy improvements in theorem proving pipelines.

Findings

Best pipeline accuracy is 36% with current models.

Corrected discrepancies increased accuracy to 70%.

Majority of failures stem from formal-informal statement misalignments.

Abstract

We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the model has to read and comprehend the problems in natural language, formalize them in Lean language, then proceed with proving the problems, and it will get credit for each problem if the formal proof corresponds to the original informal statement presented to the model. Our evaluation results reveal that the best accuracy of such pipeline can be about 36% using the SoTA models in the literature, considerably lower than the individual SoTA accuracies, 97% and 69% reported in the autoformalization and theorem proving literature. Analyzing the failure modes, we trace back a considerable portion of this drop to discrepancies between the formal and informal statements for more than half of the problems in miniF2F. We proceed with correcting all the errors, discrepancies and simplifications in formal and informal statements, and present the miniF2F-v2 with fully verified formal and informal statements and proofs. Evaluating the full theorem proving pipeline on miniF2F-v2 leads to the best accuracy of 70%, a significant improvement from the 40% on the original miniF2F, yet indicating considerable misalignment between the autoformalization models and theorem provers. Our deep analysis suggests that a higher quality benchmark can help the community better evaluate progress in the field of formal reasoning and also better diagnose the failure and success modes of autoformalization and theorem proving models. Our dataset is available at https://github.com/roozbeh-yz/miniF2F_v2.