The TPTP Problem Library and Associated Infrastructure

This paper describes the First-Order Form (FOF) and Clause Normal Form (CNF) parts of the TPTP problem library, and the associated infrastructure. TPTP v3.5.0 was the last release containing only FOF and CNF problems, and thus serves as the exemplar. This paper summarizes the history and development of the TPTP, describes the structure and contents of the TPTP, and gives an overview of TPTP related projects and tools.

[1]  Deepak Ramachandran,et al.  First-Orderized ResearchCyc : Expressivity and Efficiency in a Common-Sense Ontology , 2005 .

[2]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[3]  Geoff Sutcliffe.  Semantic Derivation Verification: Techniques and Implementation , 2006, Int. J. Artif. Intell. Tools.

[4]  Ulrich Furbach,et al.  Proceedings of the Third international joint conference on Automated Reasoning , 2006 .

[5]  Larry Wos,et al.  Experiments in Automated Deduction with Condensed Detachment , 1992, CADE.

[6]  Georg Struth,et al.  Automated Reasoning in Kleene Algebra , 2007, CADE.

[7]  Maria Paola Bonacina,et al.  On handling distinct objects in the superposition calculus , 2005, ICLP 2005.

[8]  Geoff Sutcliffe.  System Description: SystemOn TPTP , 2000, CADE.

[9]  Frances G. Livingston.  Dewey Decimal Classification and Relative Index. , 1966 .

[10]  Geoff Sutcliffe.  The CADE-21 automated theorem proving system competition , 2008, AI Commun..

[11]  Monty Newborn,et al.  Octopus: Combining Learning and Parallel Search , 2004, Journal of Automated Reasoning.

[12]  Andrei Voronkov,et al.  Encoding industrial hardware verification problems into effectively propositional logic , 2010, Formal Methods in Computer Aided Design.

[13]  J. Phillips.  Automated Theorem Proving in Loop Theory , 2008 .

[14]  Volker Sorge,et al.  Combined reasoning by automated cooperation , 2008, J. Appl. Log..

[15]  Geoff Sutcliffe,et al.  Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure , 2010, J. Formaliz. Reason..

[16]  Thomas Hillenbrand,et al.  A phytography of WALDMEISTER , 2002, AI Commun..

[17]  Geoff Sutcliffe,et al.  Smart Selective Competition Parallelism ATP , 1999, FLAIRS Conference.

[18]  Geoff Sutcliffe,et al.  TPTP, TSTP, CASC, etc , 2007, CSR.

[19]  Geoff Sutcliffe,et al.  The TPTP Problem Library , 1994, Journal of Automated Reasoning.

[20]  Michael J. Witbrock,et al.  An Introduction to the Syntax and Content of Cyc , 2006, AAAI Spring Symposium: Formalizing and Compiling Background Knowledge and Its Applications to Knowledge Representation and Question Answering.

[21]  Panagiotis Manolios,et al.  Computer-aided reasoning : ACL2 case studies , 2000 .

[22]  G. Sutcliffe,et al.  Empirically Successful Automated Reasoning in Large Theories , 2007 .

[23]  Larry Wos,et al.  Problems and Experiments for and with Automated Theorem-Proving Programs , 1976, IEEE Transactions on Computers.

[24]  Geoff Sutcliffe,et al.  The TPTP World - Infrastructure for Automated Reasoning , 2010, LPAR.

[25]  William McCune,et al.  Single axioms for groups and Abelian groups with various operations , 1993, Journal of Automated Reasoning.

[26]  Reinhold Letz,et al.  Strategy Parallelism in Automated Theorem Proving , 1998, FLAIRS.

[27]  Geoff Sutcliffe,et al.  SRASS - A Semantic Relevance Axiom Selection System , 2007, CADE.

[28]  Geoff Sutcliffe,et al.  The IJCAR ATP System Competition , 2004, Journal of Automated Reasoning.

[29]  Robert Nieuwenhuis.  The impact of CASC in the development of automated deduction systems , 2002, AI Commun..

[30]  Clark W. Barrett,et al.  The SMT-LIB Standard Version 2.0 , 2010 .

[31]  Thomas Stützle,et al.  SATLIB: An Online Resource for Research on SAT , 2000 .

[32]  Josef Urban,et al.  MPTP 0.2: Design, Implementation, and Initial Experiments , 2006, Journal of Automated Reasoning.

[33]  Geoff Sutcliffe,et al.  The state of CASC , 2006, AI Commun..

[34]  Miroslaw Truszczynski,et al.  The First Answer Set Programming System Competition , 2007, LPNMR.

[35]  Larry Wos,et al.  Set theory in first-order logic: Clauses for Gödel's axioms , 1986, Journal of Automated Reasoning.

[36]  Christoph Kreitz,et al.  The ILTP Problem Library for Intuitionistic Logic , 2007, Journal of Automated Reasoning.

[37]  Yi Gao,et al.  Automated Generation of Interesting Theorems , 2006, FLAIRS.

[38]  Lawrence C. Paulson,et al.  LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description) , 2008, IJCAR.

[39]  Francis Jeffry Pelletier,et al.  Seventy-five problems for testing automatic theorem provers , 1986, Journal of Automated Reasoning.

[40]  Michael Kohlhase,et al.  OMDoc - An Open Markup Format for Mathematical Documents [version 1.2] , 2006, Lecture Notes in Computer Science.

[41]  Gerhard Weikum,et al.  WWW 2007 / Track: Semantic Web Session: Ontologies ABSTRACT YAGO: A Core of Semantic Knowledge , 2022 .

[42]  Stephan Schulz.  Learning Search Control Knowledge for Equational Theorem Proving , 2001, KI/ÖGAI.

[43]  Michael Kohlhase,et al.  MathDox : mathematical documents on the web , 2006 .

[44]  Damien Doligez,et al.  Zenon : An Extensible Automated Theorem Prover Producing Checkable Proofs , 2007, LPAR.

[45]  Johann Schumann,et al.  Using Automated Theorem Provers to Certify Auto-generated Aerospace Software , 2004, IJCAR.

[46]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

[47]  Volker Sorge,et al.  Proof Development with OMEGA , 2002, CADE.

[48]  Geoff Sutcliffe,et al.  THF0 - The Core of the TPTP Language for Higher-Order Logic , 2008, IJCAR.

[49]  Geoff Sutcliffe.  The SZS Ontologies for Automated Reasoning Software , 2008, LPAR Workshops.

[50]  Jens Otten,et al.  leanCoP 2.0and ileanCoP 1.2: High Performance Lean Theorem Proving in Classical and Intuitionistic Logic (System Descriptions) , 2008, IJCAR.

[51]  Hans de Nivelle,et al.  A Small Framework for Proof Checking , 2008, PAAR/ESHOL.

[52]  Koen Claessen,et al.  Using the TPTP Language for Writing Derivations and Finite Interpretations , 2006, IJCAR.

[53]  David A. Plaisted,et al.  Non-Horn clause logic programming without contrapositives , 1988, Journal of Automated Reasoning.

[54]  Lawrence C. Paulson,et al.  Automation for interactive proof: First prototype , 2006, Inf. Comput..

[55]  Geoff Sutcliffe,et al.  An Interactive Derivation Viewer , 2007, UITP@FLoC.

[56]  Gerard de Melo,et al.  External Sources of Axioms in Automated Theorem Proving , 2009, KI.

[57]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[58]  Geoff Sutcliffe,et al.  Evaluating general purpose automated theorem proving systems , 2001, Artif. Intell..

[59]  William McCune,et al.  OTTER 3.3 Reference Manual , 2003, ArXiv.

[60]  Peter Baumgartner,et al.  Proceedings of the 4th international joint conference on Automated Reasoning , 2008 .

[61]  熊爱民.  Mathematical Subject Classification在数学文献信息分类中的应用 , 2004 .

[62]  Cesare Tinelli,et al.  The SMT-LIB Standard: Version 1.2 , 2005 .

[63]  Geoff Sutcliffe,et al.  First Order Reasoning on a Large Ontology , 2007, ESARLT.

[64]  Stephen F. Smith,et al.  Combining Multiple Heuristics Online , 2007, AAAI.

[65]  Konstantin Verchinine,et al.  System for Automated Deduction (SAD): A Tool for Proof Verification , 2007, CADE.

[66]  Jasmin Christian Blanchette,et al.  Three years of experience with Sledgehammer, a Practical Link Between Automatic and Interactive Theorem Provers , 2012, IWIL@LPAR.

[67]  Josef Urban,et al.  MaLARea SG1- Machine Learner for Automated Reasoning with Semantic Guidance , 2008, IJCAR.

[68]  Geoff Sutcliffe.  Progress in Automated Theorem Proving , 1997 – 1999 , 2000 .

[69]  Geoff Sutcliffe,et al.  Communication Formalisms for Automated Theorem Proving Tools , 2006 .

[70]  Aaron Stump,et al.  SMT-COMP: Satisfiability Modulo Theories Competition , 2005, CAV.

[71]  Geoff Sutcliffe,et al.  Semantic Derivation Verification , 2005, FLAIRS Conference.

[72]  Tanel Tammet.  Gandalf , 2004, Journal of Automated Reasoning.

[73]  William McCune,et al.  Ivy: a preprocessor and proof checker for first-order logic , 2000 .

[74]  Art Quaife,et al.  Automated deduction in von Neumann-Bernays-Gödel set theory , 1992, Journal of Automated Reasoning.

[75]  Helmut Veith,et al.  Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning , 2010, ICLP 2010.

[76]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[77]  Toby Walsh,et al.  CSPLIB: A Benchmark Library for Constraints , 1999, CP.

[78]  Frank Pfenning,et al.  TPS: A theorem-proving system for classical type theory , 1996, Journal of Automated Reasoning.

[79]  Geoff Sutcliffe,et al.  Extending the TPTP Language to Higher-Order Logic with Automated Parser Generation , 2006, IJCAR.

[80]  Geoff Sutcliffe,et al.  Integration of the TPTPWorld into SigmaKEE , 2008, PAAR/ESHOL.