How Much Should This Symbol Weigh? A GNN-Advised Clause Selection

Abstract

Clause selection plays a crucial role in modern saturation-based automatic theorem provers. A commonly used heuristic suggests prioritizing small clauses, i.e., clauses with few symbol occurrences. More generally, we can give preference to clauses with a low weighted symbol occurrence count, where each symbol’s occurrence count is multiplied by a respective symbol weight. Traditionally, a human domain expert would supply the symbol weights.In this paper, we propose a system based on a graph neural network that learns to predict symbol weights with the aim of improving clause selection for arbitrary first-order logic problems. Our experiments demonstrate that by advising the automatic theorem prover Vampire on the first-order fragment of TPTP using a trained neural network, the prover’s problem solving capability improves by 6.6% compared to uniformly weighting symbols and by 2.1% compared to a goal-directed variant of the uniformly weighting strategy.