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A First Class Boolean Sort in First-Order Theorem Proving and TPTP [chapter]

Evgenii Kotelnikov, Laura Kovács, Andrei Voronkov
2015 Lecture Notes in Computer Science
In this paper, we present an extension FOOL of many-sorted first-order logic, in which the boolean sort is treated as a first-class sort.  ...  However, in the TPTP language, the input language of automated first-order theorem provers, the use of the boolean sort is limited compared to other sorts, thus hindering the use of first-order theorem  ...  In Section 5 we discuss the support of the boolean sort in TPTP and propose changes to it required to support a first-class boolean sort.  ...

The vampire and the FOOL

Evgenii Kotelnikov, Laura Kovács, Giles Reger, Andrei Voronkov
2016 Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2016
This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays.  ...  In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions.  ...  Section 2 extends the TPTP language of monomorphic many-sorted first-order formulas, called TFF0 [19] , and allows users to treat the built-in boolean sort \$o as a first class sort.  ...

The TPTP Typed First-Order Form with Arithmetic [chapter]

Geoff Sutcliffe, Stephan Schulz, Koen Claessen, Peter Baumgartner
2012 Lecture Notes in Computer Science
The TPTP World is a well established infrastructure supporting research, development, and deployment of Automated Theorem Proving systems.  ...  Recently, the TPTP World has been extended to include a typed first-order logic, which in turn has enabled the integration of arithmetic. This paper describes these developments. 8  ...  Acknowledgments: Alexandre Riazanov did the analysis of TPTP CNF problems for implicit type information. Michael Schick and Peter Watson produced many of the TFF and arithmetic problems.  ...

SMTtoTPTP – A Converter for Theorem Proving Formats [chapter]

Peter Baumgartner
2015 Lecture Notes in Computer Science
The TPTP TFF format is an extension of the TPTP format widely used by automated theorem provers, adding a sort system and arithmetic theories.  ...  SMTtoTPTP is a converter from proof problems written in the SMT-LIB format into the TPTP TFF format.  ...  The distribution includes the Scala 3 source code and a ready-to-run Java jar-file. SMTtoTPTP can also be used as a library for parsing SMT-LIB files into an abstract syntax tree.  ...

Faster, Higher, Stronger: E 2.3 [chapter]

Stephan Schulz, Simon Cruanes, Petar Vukmirović
2019 Lecture Notes in Computer Science
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation.  ...  We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via  ...  Introduction E is a fully automated theorem prover for first-order logic with equality.  ...

Faster, Higher, Stronger

Bruce K. Rubin
2013 American Journal of Respiratory and Critical Care Medicine
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation.  ...  We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via  ...  Introduction E is a fully automated theorem prover for first-order logic with equality.  ...

Beagle – A Hierarchic Superposition Theorem Prover [chapter]

Peter Baumgartner, Joshua Bax, Uwe Waldmann
2015 Lecture Notes in Computer Science
Beagle is an automated theorem prover for first-order logic modulo built-in theories. It implements a refined version of the hierarchic superposition calculus.  ...  only give a brief overview of the calculus and of the semantics of hierarchic specifications.  ...  Hierarchic Theorem Proving Hierarchic superposition [2, 7] is a calculus for automated reasoning in a hierarchic combination of first-order logic and some background theory. 3 We assume that we have  ...

LEO-II and Satallax on the Sledgehammer test bench

Nik Sultana, Jasmin Christian Blanchette, Lawrence C. Paulson
2013 Journal of Applied Logic
Sledgehammer is a tool that harnesses external first-order automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL.  ...  To explore their usefulness, these ATPs are measured against first-order ATPs and built-in Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library.  ...  Geoff Sutcliffe drove the development of TPTP THF0 and was involved in many discussions in connection with this paper.  ...

Experiments on Supporting Interactive Proof Using Resolution [chapter]

Jia Meng, Lawrence C. Paulson
2004 Lecture Notes in Computer Science
In particular, we present a sound and practical encoding in first-order logic of Isabelle's type classes.  ...  Interactive theorem provers can model complex systems, but require much effort to prove theorems.  ...  Acknowledgements We are grateful to the Vampire team (Alexandre Riazanov and Andrei Voronkov) for their co-operation and to Gernot Stenz and Geoff Sutcliffe for running some of our problems on their reasoning  ...

Extensional Crisis and Proving Identity [chapter]

Ashutosh Gupta, Laura Kovács, Bernhard Kragl, Andrei Voronkov
2014 Lecture Notes in Computer Science
In this paper we show how addition of a new inference rule, called extensionality resolution, allows first-order theorem provers to easily solve problems no modern first-order theorem prover can solve.  ...  Extensionality resolution helps VAMPIRE to solve problems from the TPTP library of first-order problems that were never solved before by any prover.  ...  S11402-N23 and S11410-N23), and the WWTF PROSEED grant ICT C-050.  ...

Extensional Higher-Order Paramodulation in Leo-III [article]

Alexander Steen, Christoph Benzmüller
2021 arXiv   pre-print
Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.  ...  The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers.  ...  In contrast to first-order theorem proving, it is hence necessary to interleave syntactical unification and (semantical) proof search, which is more difficult to control in practice.  ...

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these tools.  ...  The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians to prove theorems by computer programs.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ...

Stålmarck's algorithm as a HOL derived rule [chapter]

John Harrison
1996 Lecture Notes in Computer Science
Here we describe the algorithm and explore its implementation as a HOL derived rule.  ...  Stålmarck's algorithm is a patented technique for tautology-checking which has been used successfully for industrial-scale problems.  ...  explaining the algorithm in detail and providing stimulating discussions about this and many other topics.  ...