The Tptp Problem Library And Associated Infrastructure

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The TPTP Problem Library and Associated Infrastructure: A Comprehensive Resource for Automated Theorem Proving

The TPTP problem library is the de facto standard set of test problems for classical logic Automated Theorem Proving (ATP) systems. It provides a comprehensive collection of problems in various formats, such as Clause Normal Form (CNF), First-Order Form (FOF), Typed First-order Form (TFF), and Typed Higher-order Form (THF). The TPTP problem library is supported by a rich infrastructure of standards, tools, and linked projects, collectively known as the "TPTP world".

In this article, we will give an overview of the TPTP problem library and associated infrastructure, focusing on its history, structure, contents, and applications. We will also highlight some of the challenges and opportunities for future development and research in this area.

History and Development of the TPTP Problem Library

The TPTP problem library was initiated in 1993 by Geoff Sutcliffe as a way to provide a common basis for meaningful empirical evaluation of classical logic ATP systems. The first release of the TPTP contained 750 problems in CNF format, mostly collected from existing sources such as the CADE ATP System Competition (CASC) and the LTB Library for Automated Deduction. Since then, the TPTP has grown steadily in size and scope, incorporating new problems from various domains and sources, as well as new formats and features to accommodate different types of logic and reasoning.

The current version of the TPTP is v8.4.0, released in December 2020. It contains 43,538 problems in 11 different formats: CNF, FOF, TFF0 (monomorphic typed first-order), TFF1 (polymorphic typed first-order), THF0 (monomorphic typed higher-order), THF1 (polymorphic typed higher-order), TF0 (monomorphic typed first-order with arithmetic), TF1 (polymorphic typed first-order with arithmetic), TH0 (monomorphic typed higher-order with arithmetic), TH1 (polymorphic typed higher-order with arithmetic), and PCNF (polynomial CNF). The problems are organized into 56 domains, ranging from abstract algebra to verification.

The TPTP problem library is managed in the manner of a software product, with fixed releases identified by a release number in the form vVersion.Edition.Patch. The Version enumerates major new releases of the TPTP in which important new features have been added. The Edition is incremented each time new problems are added to the current version. The Patch level is incremented each time errors found in the current edition are corrected. The TPTP web site http://www.tptp.org provides access to all components of the TPTP world, including the TPTP problem library download package, a quick-guide introduction and detailed documentation for the TPTP, online browsing of the TPTP problems and their solutions, an interface for running ATP systems on problems and post-processing the solutions, and links to a range of related projects.

Structure and Contents of the TPTP Problems

A TPTP problem is a text file that contains one or more logical formulas that represent a conjecture to be proved or a set of axioms to be used for proving. Each problem has a unique name that consists of three letters indicating the domain, followed by three digits indicating the number within the domain. For example, ALG001 is the first problem in the abstract algebra domain. Each problem also has a status that indicates whether it is satisfiable or unsatisfiable (for CNF problems), or whether it has a proof or a countermodel (for FOF and higher-order problems).

A TPTP problem file consists of four sections: language, formula selection directives, include directives, and formulas. The language section specifies the format of the problem, such as CNF or THF1. The formula selection directives indicate which formulas are relevant for proving or refuting the conjecture. The include directives allow a problem to import formulas from other problems or from standard libraries. The formulas section contains the actual logical formulas that make up the problem.

A logical formula in the TPTP has a name aa16f39245