The Computer Journal ( IF 1.077 ) Pub Date : 2021-05-03 , DOI: 10.1093/comjnl/bxab030
Maximiliano Cristiá, Ricardo D Katz, Gianfranco Rossi

|\$\{log\}\$| (‘setlog’) is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FS&RA). As such, it can be used as an automated theorem prover for this theory. |\$\{log\}\$| is able to automatically prove a number of FS&RA theorems, but not all of them. Nevertheless, we have observed that many theorems that |\$\{log\}\$| cannot automatically prove can be divided into a few subgoals automatically dischargeable by |\$\{log\}\$|⁠. The purpose of this work is to present a prototype interactive theorem prover (ITP), called |\$\{log\}\$|-ITP, providing evidence that a proper integration of |\$\{log\}\$| into world-class ITP’s can deliver a great deal of proof automation concerning FS&RA. An empirical evaluation based on 210 theorems from the TPTP and Coq’s SSReflect libraries shows a noticeable reduction in the size and complexity of the proofs with respect to Coq.

| \$ \ {log \} \$ | （'setlog'）是有限集和有限集关系代数（FS＆RA）理论公式的可满足性求解器。这样，它可以用作该理论的自动定理证明者。| \$ \ {log \} \$ | 能够自动证明许多FS＆RA定理，但不是全部。但是，我们已经观察到许多定理，即| \$ \ {log \} \$ | 不能自动证明的| ||可| \$ \ {log \} \$ |⁠划分为几个子目标。这项工作的目的是介绍一个称为| \$ \ {log \} \$ |的原型交互式定理证明器（ITP）-ITP，提供证明| \$ \ {log \} \$ |正确整合的证据进入世界一流的ITP可以提供有关FS＆RA的大量证明自动化。根据TPTP和Coq的SSReflect库中的210个定理进行的经验评估表明，与Coq相比，证明的大小和复杂性显着降低。

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