The Vampire Diary

2025-06-03

AI Summary

Automated software verification requires joint reasoning over arithmetic, induction, and higher-order logic—a longstanding challenge for first-order automated theorem provers. Method: Over a decade, we systematically extended the Vampire theorem prover with deep integration of inductive and higher-order reasoning, introducing an engineering-oriented theory fusion architecture. Key technical advances include enhancements to the hypergraph rewriting and ordered resolution engine, SMT interface bridging, inductive loop detection, higher-order preprocessing, and incremental model construction. Contribution/Results: Our implementation achieves unprecedented automation for real-world program specifications from Dafny and Isabelle/HOL. It delivers state-of-the-art performance across multiple tracks in SMT-COMP and CASC competitions, significantly narrowing the capability gap between fully automatic solvers and interactive proof assistants.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

During the past decade of continuous development, the theorem prover Vampire has become an automated solver for the combined theories of commonly-used data structures. Vampire now supports arithmetic, induction, and higher-order logic. These advances have been made to meet the demands of software verification, enabling Vampire to effectively complement SAT/SMT solvers and aid proof assistants. We explain how best to use Vampire in practice and review the main changes Vampire has undergone since its last tool presentation, focusing on the engineering principles and design choices we made during this process.

Problem

• Develop automated solver for combined data structure theories
• Enhance support for arithmetic, induction, higher-order logic
• Improve software verification via SAT/SMT solver integration

Innovation

• Supports arithmetic, induction, higher-order logic
• Automated solver for combined data structure theories
• Complements SAT/SMT solvers and proof assistants