NeurIPS 2025

3D-Prover: Diversity Driven Theorem Proving With
Determinantal Point Processes
Sean Lamont1,2, Christian Walder3, Amir Dezfouli4, Paul Montague2, Michael Norrish1
1Australian National University
2Defence Science and Technology Group
3Google DeepMind
4BIMLOGIQ
sean.lamont@anu.edu.au
Abstract
A key challenge in automated formal reasoning is the intractable search space,
which grows exponentially with the depth of the proof. This branching is caused
by the large number of candidate proof tactics which can be applied to a given
goal. Nonetheless, many of these tactics are semantically similar or lead to an
execution error, wasting valuable resources in both cases. We address the problem
of effectively pruning this search, using only synthetic data generated from previous
proof attempts. We first demonstrate that it is possible to generate semantically
aware tactic representations which capture the effect on the proving environment,
likelihood of success, and execution time. We then propose a novel filtering
mechanism which leverages these representations to select semantically diverse
and high quality tactics, using Determinantal Point Processes. Our approach, 3D-
Prover, is designed to be general, and to augment any underlying tactic generator.
We demonstrate the effectiveness of 3D-Prover on the miniF2F and LeanDojo
benchmarks by augmenting popular open source proving LLMs. We show that
our approach leads to an increase in the overall proof rate, as well as a significant
improvement in the tactic success rate, execution time and diversity. We make our
code available at https://github.com/sean-lamont/3D-Prover.
1
Introduction
Interactive Theorem Proving (ITP) traditionally involves a human guiding an ITP system to verify a
formal proposition. The applications range from secure software (Tan et al., 2019) to the verification
of mathematical results (Hales et al., 2017). There has been significant interest in automating this
process, with formalization efforts requiring ...