🤖 AI Summary
To address the undecidability induced by quantifiers in first-order logic (FOL), this paper proposes a machine learning–driven dynamic quantifier instantiation method integrated into the cvc5 SMT solver. The method operates during solving via multi-round, adaptive quantifier activation decisions—determining when and which quantified formulas to instantiate based on evolving solver state. It employs lightweight gradient-boosted tree models (XGBoost/LightGBM), tightly coupled with cvc5’s architecture to enable embedded, real-time ML inference and online incremental policy prediction. Trained on a large-scale dataset derived from the Mizar Mathematical Library, the approach significantly improves cvc5’s performance on holdout benchmarks: solving success rates increase markedly—especially for FOL problems featuring complex quantifier structures—thereby alleviating the quantifier-induced performance bottleneck in automated reasoning.
📝 Abstract
In this work we considerably improve the state-of-the-art SMT solving on first-order quantified problems by efficient machine learning guidance of quantifier selection. Quantifiers represent a significant challenge for SMT and are technically a source of undecidability. In our approach, we train an efficient machine learning model that informs the solver which quantifiers should be instantiated and which not. Each quantifier may be instantiated multiple times and the set of the active quantifiers changes as the solving progresses. Therefore, we invoke the ML predictor many times, during the whole run of the solver. To make this efficient, we use fast ML models based on gradient boosting decision trees. We integrate our approach into the state-of-the-art cvc5 SMT solver and show a considerable increase of the system's holdout-set performance after training it on a large set of first-order problems collected from the Mizar Mathematical Library.