We discuss the practical results obtained by the first generation of automated theorem provers based on Deduction modulo theory. In particular, we demonstrate the concrete improvements such a framework can bring to first-order theorem provers with the introduction of a rewrite feature. Deduction modulo theory is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewrite rules. We introduce two automated reasoning systems that have been built to extend other provers with Deduction modulo theory. The first one is Zenon Modulo, a tableau-based tool able to deal with polymorphic first-order logic with equality, while the second one is iProverModulo, a resolution-based system dealing with first-order logic with equality. We also provide some experimental results run on benchmarks that show the beneficial impact of the extension on these two tools and their underlying proof search methods. Finally, we describe the two backends of these systems to the Dedukti universal proof checker, which also relies on Deduction modulo theory, and which allows us to verify the proofs produced by these tools.

中文翻译：

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一阶自动理论推理：当演绎模理论遇上实践

我们讨论了基于演绎模理论的第一代自动定理证明器获得的实际结果。特别是，我们展示了这种框架可以通过引入重写功能为一阶定理证明者带来的具体改进。演绎模理论是谓词演算的扩展，重写了术语和命题。它非常适合理论中的证明搜索，因为它将许多公理转化为重写规则。我们介绍了两个自动推理系统，这些系统旨在通过演绎模理论扩展其他证明者。第一个是 Zenon Modulo，一个基于表格的工具，能够处理具有相等性的多态一阶逻辑，而第二个是 iProverModulo，一个基于分辨率的系统，处理具有相等性的一阶逻辑。我们还提供了一些在基准测试上运行的实验结果，这些结果显示了扩展对这两个工具及其底层证明搜索方法的有益影响。最后，我们将这些系统的两个后端描述给 Dedukti 通用证明检查器，它也依赖于演绎模理论，并允许我们验证这些工具生成的证明。