Many applications of formal methods require automated reasoning about system properties, such as system safety and security. To improve the performance of automated reasoning engines, such as SAT/SMT solvers and first-order theorem prover, it is necessary to understand both the successful and failing attempts of these engines towards producing formal certificates, such as logical proofs and/or models. Such an analysis is challenging due to the large number of logical formulas generated during proof/model search. In this paper we focus on saturation-based first-order theorem proving and introduce the SATVIS tool for interactively visualizing saturation-based proof attempts in first-order theorem proving. We build SATVIS on top of the world-leading theorem prover VAMPIRE, by interactively visualizing the saturation attempts of VAMPIRE in SATVIS. Our work combines the automatic layout and visualization of the derivation graph induced by the saturation attempt with interactive transformations and search functionality. As a result, we are able to analyze and debug (failed) proof attempts of VAMPIRE. Thanks to its interactive visualisation, we believe SATVIS helps both experts and non-experts in theorem proving to understand first-order proofs and analyze/refine failing proof attempts of first-order provers.

中文翻译：

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Vampire 中饱和尝试的交互式可视化

形式方法的许多应用都需要对系统属性（例如系统安全性和安保性）进行自动推理。为了提高自动推理引擎（例如 SAT/SMT 求解器和一阶定理证明器）的性能，有必要了解这些引擎在生成正式证书（例如逻辑证明和/或模型）方面的成功和失败尝试。由于在证明/模型搜索期间生成了大量逻辑公式，因此这种分析具有挑战性。在本文中，我们专注于基于饱和度的一阶定理证明，并介绍了 SATVIS 工具，用于交互式可视化一阶定理证明中基于饱和度的证明尝试。我们通过在 SATVIS 中交互式可视化 VAMPIRE 的饱和尝试，在世界领先的定理证明器 VAMPIRE 之上构建 SATVIS。我们的工作将饱和尝试引起的派生图的自动布局和可视化与交互式转换和搜索功能相结合。因此，我们能够分析和调试 VAMPIRE 的（失败的）证明尝试。由于其交互式可视化，我们相信 SATVIS 可以帮助定理证明中的专家和非专家理解一阶证明并分析/改进一阶证明者的失败证明尝试。