Lecture Notes in Artificial Intelligence 814

Subseries of Lecture Notes in Computer Science

Edited by J. G. Carbonell and J. Siekmann

Lecture Notes in Computer Science Edited by G. Goos and J. Hartmanis

Alan Bundy (Ed.)

Automated Deduction CADE-12

12th International Conference on Automated Deduction Nancy, France, June 26 - July 1, 1994 Proceedings

Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest

Series Editors

Jaime G. Carbonell School of Computer Science, Carnegie Mellon University Schenley Park, Pittsburgh, PA 15213-3890, USA

JSrg Siekmann University of Saarland German Research Center for Artificial Intelligence (DFKI) Stuhlsatzenhausweg 3, D-66123 Saarbriicken, Germany

Volume Editor

Alan Bundy Department of Artificial Intelligence, The University of Edinburgh 80 South Bridge, Edinburgh EH 1 1HN, United Kingdom

CR Subject Classification (1991):I.2.3, E4.1-2

ISBN 3-540-58156-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-58156-1 Springer-Verlag New York Berlin Heidelberg

CIP data applied for.

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�9 Springer-Verlag Berlin Heidelberg 1994 Printed in Germany

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P r e f a c e

This volume contains the papers presented at the Twelfth International Con- ference on Automated Deduction (CADE-12) held on June 26-July 1, 1994, at the Palais des Congr~s de Nancy, France, sponsored by CADE Inc. and hosted by INRIA and CRIN; many other organizations provided co-sponsorship. The CADE conferences are the major forum for the presentation of new research in all aspects of automated deduction.

There were 177 papers submitted to CADE-12:152 regular papers, 23 system descriptions and 2 problem sets. Of these 177 papers, 67 were accepted: 46 reg- ular papers, 19 system descriptions and 2 problem sets (some papers switched categories during refereeing). In addition, the CADE-12 programme contained 3 invited talks, a banquet speech, a panel discussion, 7 workshops and 8 tutori- als. The number of papers submitted and accepted are both records for CADE conferences. The field of automated deduction is clearly growing. This growth has been achieved with no dilution of the very high standards in the field. In particular, the quality of papers accepted by CADE-12 is at least as high as at previous CADEs. This volume presents many of the most important research results in automated deduction since CADE-11.

Much of the growth is accounted for by the spread of interest in the field around the globe. CADE-12 received papers from: Australia, Austria, Bel- gium, Canada, France, Germany, Italy, Japan, Norway, China, Poland, Portugal, Spain, Sweden, The Netherlands, UK, USA and Ukraine.

Since CADE-11, the CADE conference series has been put on a firmer footing with the incorporation of CADE. CADE Inc. will sponsor all future CADE conferences. It will protect the officers of CADE from financial liability and provide initial funding for CADE conferences as well as providing a holding fund for any surpluses. CADE Inc. is a sub-corporation of the Association of Automated Reasoning. It will be run by a Board of Trustees consisting of the current and past four CADE Programme Chairs plus a Secretary and Treasurer. I am particularly grateful to Nell Murray for agreeing to hold the joint post of Secretary and Treasurer of CADE Inc.

I would like to thank the many people who made CADE-12 possible. I am grateful: to the Programme Committee and the additional referees they recruited for reviewing a record number of papers to a very high standard in a short time scale; to Claude Kirchner and his Local Arrangements Committee for their en- ergy and dedication in organising an excellent conference; to my fellow Trustees for their advice and encouragement, especially to Secretary/Treasurer Neil Mur- ray; to the Invited Speakers, John Slaney, Ursula Martin and Bob Constable, the Banquet Speaker, Richard Platek, and the Panel Organiser, Bob Boyer; to the tutorial and workshop organisers; to Janice Lonsdale for help in organising the Programme Committee Meeting at Imperial College; a~d last, but by no means least, to Ian Green, Millie Tupman, Carole Douglas and the members of my research group at Edinburgh, who helped with the myriad administrative tasks involved in programme chairing a conference.

Alan Bundy CADE-12 Programme Chair

Yl

Herbrand Award for Distinguished Contributions to Automated Reasoning

Recipient: Professor W. W. Bledsoe

We are delighted to announce that the second Herbrand Award for Distinguished Contributions to Automated Reasoning will be given at CADE-12 to Professor Woody Bledsoe, of the University of Texas at Austin. The Herbrand Award was initiated at CADE-11 to honour an individual or (a group of) individuals for exceptional contributions to the field of Automated Deduction. The winner is selected by the Trustees, the Programme Committee and previous winners. At CADE-11 the Award was made to Dr. Larry Wos. Woody Bledsoe has made numerous contributions to the field of Automated Deduction including natural proof systems, interactive systems, decision procedures, analogical reasoning and applications to set theory, analysis and program verification. He has been a source of inspiration to generations of researchers at Austin and throughout the world.

Nomination for this award can be made at any time to the CADE chair. A nomination should include a letter (of up to 2000 words) from a principal nominator describing the nominee's contributions, along with two other letters (of up to 2000 words) of endorsement.

Previous CADEs

CADE-1 Argonne National Laboratory, USA, 1974 (IEEE Transactions on Com- puters C-25, #8).

CADE-2 Oberwolfach, Germany, 1976. CADE-3 MIT, USA, 1977. CADE-4 University of Texas at Austin, USA, 1979. CADE-5 Les Arcs, France, 1980 (Springer-Verlag LNCS 87).

CADE-6 Courant Institute, New York, USA, 1982 (Springer-Verlag LNCS 138). CADE-7 Napa, California, USA, 1984 (Springer-Verlag LNCS 170). CADE-8 University of Oxford, UK, 1986 (Springer-Verlag LNCS 230). CADE-9 Argonne National Laboratory, USAr 1988 (Springer-Verlag LNCS 310). CADE-10 Kaiserslautern, Germany, 1990 (Springer-Verlag LNAI 449). CADE-11 Saratoga Springs, USA, 1992 (Springer-Verlag LNAI 607).

VII

CADE Inc. trustees Alan Bundy (Chair) Neff Murray (Secretary/Treasurer) Deepak Kapur (CADE-11) Mark Stickel (CADE-10) Ewing Lusk (CADE-9) J6rg Siekmann (CADE-8)

University of Edinburgh State University of New York at Albany State University of New York at Albany SRI International Argonne National Laboratory UniversitSt Kaiserslautern

Programme chair

Alan Bundy University of Edinburgh

Assis tant to p rog ramme chair

Ian Green University of Edinburgh

Programme commi t tee

Luigia Carlucci Aiello Jfirgen Avenhaus David Basin Wolfgang Bibel Francois Bry Ricardo Caferra Edmund Clarke Anthony Cohn William Farmer Alan Frisch Dov Gabbay Harald Ganzinger Stephen Garland Fausto Giunchiglia Mike Gordon Elsa Gunter Masami Hagiya Ryuzo Hasegawa Larry Henschen Larry Hines Steffen HSlldobler Douglas Howe Matt Kaufmann H~l~ne Kirchner Alexander Leitsch Ursula Martin David McAllester William McCune Michael McRobbie Tobias Nipkow Itans-Jiirgen Ohlbach

Universit5 di Roma "La Sapienza" Universitiit Kaiserslautern Max-Planck-Institut fiir Informatik, Saarbriicken Technische Hochschule Darmstadt Ludwig-Maximilians- UniversitSt Miinchen LIFIA-IMA G Carnegie Mellon University University of Leeds The MITRE Corporation University of York Imperial College Max-Planck-Institut ]iir Informatik, Saarbriicken MIT IRST ~ University of Trento University of Cambridge A T~A T Bell Laboratories University of Tokyo Institute for New Generation Computer Technology Northwestern University University of Texas at Austin Technische UniversitSt Dresden A T ~ T Bell Laboratories Computational Logic Inc. CRIN- CNRS ~A INRIA Lorraine Technische Universitiit Wien University o/ St. Andrews MIT Argonne National Laboratory The Australian National University Technische Universitiit Miinchen Max-Planck-Institut fiir Informatik, Saarbriicken

VIII

P r o g r a m m e c o m m i t t e e

William Pase Alberto Pettorossi Frank Pfenning David Plaisted Uday Reddy Michael Rusinowitch Taisuke Sato Ken Satoh Natarajan Shankar John Slaney Alan Smaill Gert Smolka Andrei Voronkov Richard Waldinger Lincoln Wallen Christoph Walther

Alessandro Armando Leo Bachmair Jonas Barklund Peter Barth Antje Beringer Bob Boyer Stefan Brrining Bruno Buchberger Marco Cadoli Alessandro Cimatti Pierangelo Dell'Acqua JSrg Denzinger Francesco M. Donini Uwe Egly Norbert Eisinger Amy Felty Chris FermriUer Hiroshi Fujita Ulrich Furbach- Stefan Gerberding Jrirgen Giesl Enrico Giunchiglia John Gooday Mark Grundy Ursula Halls Hirotaka Hara Robert Hasker Kouji Iwanuma Jrirgen Janas

( c o n t d . )

ORA Canada Universitd di Roma Tot Vergata Carnegie Mellon University UNC Chapel Hill ~ MPI f~r In]ormatik, 8aarbr~cken University of Illinois at Urbana-Champaign CRIN-INRIA Electrotechnical Laboratory Fujitsu Laboratories Ltd. SRI International The Australian National University University of Edinburgh DFKI ~ UniversitSt des Saarlandes, Saarbr~cken Uppsala University SRI International University of Oxford Technisehe Hoehsehule Darmstadt

R e f e r e e s

Deepak Kaput Hans Kleine Brining Eckhard Koch Christoph Kreitz Sentot Kromodimoeljo Reinhold Letz Craig MacNish Paolo Mancarella M. MarteUi Ron van der Meyden J Moore Kunaki Mukai Daniele Nardi Paliath Narendran Nicola Olivetti Eugenio Omodeo Uwe Petermann William Pierce Fiora Pirri Katalin Prasser Christian Prehofer Maurizio Proietti Martin Protzen Thomas Rath Horst Reichel Michael M. Richter Mark Saaltink Ko Sakai

Gernot Salzer Manfred Schmidt-Schaufl Peter H. Schmitt Josef Schneeberger Johann Schumann Roberto Sebastiani Luciano Serafini Ute Sigmund Don Simon Mark Stickel Jrirgen Stuber Sakthi Subramanian Christian Suttner Toshihisa Takagi Kazuko Takahashi Yukihide Takayama Michael Thielscher Paul Thistlewaite Yozo Toda Paolo Traverso Ralf Treinen Haruyasu Ueda Adolfo Villafiorita JSrg Wrirtz Uwe Waldmann Emile Weydert Matt Wilding Jia-Huai You Bill Young

Ix

Robert L. Constable Ursula Martin Richard Platek John Slaney

Invited speakers Cornell University University of St. Andrews Odyssey Research Associates ~ Cornell University The Australian National University

L o c a l a r r a n g e m e n t s c o m m i t t e e

Claude Kirchner (Chair) Anne-Lise Charbonnier Miki Hermann Eric Domenjoud Armelle Savary

Assistance with refereeing process Josie Bundy Weiru Liu Ian Frank Raul Monroy Ian Gent Santiago Negrete Ian Green Julian Richardson Andrew Ireland Alan Smaill Ina Kraan Geraint Wiggins

Sponsor CADE Inc.

H o s t

INRIA Lorraine & CRIN

Co-sponsors

Department of Artificial Intelligence, University of Edinburgh

CCL Esprit Working Group Computational Logic Inc. CNET CNRS-SPI Conseil Gdndral de Meurthe et Moselle Conseil Rdgional de Lorraine District de l'agglom~ration Nancdenne

Institut National Polytechnique de Lorraine

Minist~re de l'Enseignement Supdrieur et de la Recherche

Sun Microsystems Universitd de Nancy I Universitd de Nancy II Ville de Nancy Ville de Villers l~s Nancy

With the cooperation of

CEBEA Nogema Hewlett Packard OC]~ IBM Summer Systems

The International Joint Conference on Artificial Intelligence, Inc.

T a b l e o f c o n t e n t s

Invited talk The crisis in finite mathematics: Automated reasoning as cause and cure . . . . . 1

John Slaney (The Australian National University)

Heuristics for induction A divergence critic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Toby Walsh (INRIA Lorraine) Synthesis of induction orderings for existence proofs . . . . . . . . . . . . . . . . . . . . . . . . 29

Dieter I-Iutter (DFKI Saarbriieken) Lazy generation of induction hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Martin Protzen (Technische IIoehschule Darmstadt)

Experiments with resolution systems The search efficiency of theorem proving strategies . . . . . . . . . . . . . . . . . . . . . . . . . 57

David A. Plaisted (University of North Carolina at Chapel Hill) A method for building models automatically: Experiments with an extension of O T T E R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Christophe Bourely, Ricardo Caferra and Nicolas Peltier (LIFIA-IMA G) Model elimination without contrapositives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Peter Baumgartner and Ulrich Furbach (Universitiit Koblenz)

Implicit vs. explicit induction Induction using term orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Francois Bronsard, Uday S. Reddy and Robert W. Hasker (The University of Illinois at Urbana-Champaign)

Mechanizable inductive proofs for a class of V B formulas . . . . . . . . . . . . . . . . . . . 118 Jacques Chazarain and Emmanuel Kounalis (Universitd de Nice Sophia Antipolis)

On the connection between narrowing and proof by consistency . . . . . . . . . . . . 133 Olav Lysne (University of Oslo)

Induction A fixedpoint approach to implementing (co)inductive definitions . . . . . . . . . . . 148

Lawrence C. Paulson (University of Cambridge) On notions of inductive validity for first-order equational clauses . . . . . . . . . . . 162

Claus-Peter Wirth and Bernhard Gramlich (Universitdt Kaiserslautern) A new application for explanation-based generalisation within automated deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Siani Baker (University of Cambridge)

•

Heuristics for controlling resolution Semantically guided first-order theorem proving using hyper-linking . . . . . . . 192

Heng Chu and David A. Plaisted (University of North Carolina at Chapel Hill)

The applicability of logic program analysis and t ransformation to theorem proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

D.A. de Waal and J.P. Gallagher (University of Bristol) Detecting non-provable goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Stefan Bri~ning (Teehnische Hochsehule Darmstadt)

Panel discussion A mechanically proof-checked encyclopedia of mathematics: Should we build one? Can we? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Robert S. Boyer (University of Texas at Austin ~ Computational Logic, Inc.), N.G. de Bruijn (Eindhoven University of Technology), Gdrard Huet (INRIA Rocquencourt) and Andrzej Trybulec (Warsaw University in Biatystok)

ATP problems The T P T P problem library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Geoff Suteliffe (James Cook University), Christian Suttner and Theodor Yemenis ( Teehnische Universitdt Miinchen)

Unification Combinat ion techniques for non-disjoint equational theories . . . . . . . . . . . . . . . 267

Eric Domenjoud, Francis Klay and Christophe Ringeissen (CRIN-CNRS INRIA Lorraine)

Primal g rammars and unification modulo a binary clause . . . . . . . . . . . . . . . . . . 282 Gernot Salzer (Teehnisehe Universitdt Wien)

Logic programming applications Conservative query normalization on parallel circumscription . . . . . . . . . . . . . . 296

Kouji Iwanuma ( Yamanashi University) Bot tom-up evaluation of datalog programs with ari thmetic constraints . . . . . 311

Laurent Fribourg and Marcos Veloso Peixoto (LIENS Paris) On intuitionistic query answering in description bases . . . . . . . . . . . . . . . . . . . . . 326

Veronique Royer (ONERA, Chatillon) and J. Joachim Quantz ( Technische Universit~it Berlin)

Applications Deductive composition of astronomical software from subroutine l ibraries. . 341

Mark Stiekel, Richard Waldinger (SRI International), Michael Lowry, Thomas Pressburger and Ian Underwood (NASA Ames Research Center)

Xll l

P r o o f script pragmat ics in IMPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 William M. Farmer, Joshua D. Guttman , Mark E. Nadel and F. Javier Thayer (The MITRE Corporation)

A mechaniza t ion of s t rong Kleene logic for part ial functions . . . . . . . . . . . . . . . 371 Manfred Kerber and Michael Kohlhase (Universitiit des Saarlandes)

S p e c i a l - p u r p o s e p r o v e r s

Algebraic factor ing and geometry theorem proving . . . . . . . . . . . . . . . . . . . . . . . . 386 Dongming Wang (Institut IMA G)

Mechanical ly proving geometry theorems using a combinat ion of Wu's m e t h o d and Collins' me thod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Nicholas Freitag McPhee (University of Minnesota), Shang-Ching Chou and Xiao-Shan Gao (The Wichita State University)

StrSrve and integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Larry M. Hines (University of Texas at Austin)

B a n q u e t s p e e c h

W h a t is a proof? . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Richard Platek (Odyssey Research Associates ~ CorneU University)

I n v i t e d t a l k Terminat ion, geomet ry and invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

Ursula Martin (University of St. Andrews)

R e w r i t e r u l e t e r m i n a t i o n Ordered chaining for total orderings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

Leo Bachmair (SUNY at Stony Brook) and Harald Ganzinger (Max-Planck-Institut jffir Informatik, SaarbrScken)

Simple t e rmina t ion revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Aart Middeldorp (University of Tsukuba) and Hans Zantema (Utrecht University)

Terminat ion orderings for rippling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 David A. Basin (Max-Planck-Institut fiir Informatik, Saarbr5cken) and Toby Walsh (INRIA Lorraine)

ATP efficiency A novel asynchronous parallelism scheme for first-order logic ............... 484

David B. Sturgill and Alberto Maria Segre (Cornell University) Proving with BDDs and control of informat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Jean Goubault (Bull Corporate Research Center) Extended path- indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

Peter Graf (Max.Planck-Institut fiir Informatik, Saarbr(tcken)

XIV

I n v i t e d t a l k Export ing and reflecting abst ract metamathemat ics . . . . . . . . . . . . . . . . . . . . . . . 529

Robert L. Constable (Cornell University)

A C u n i f i c a t i o n Associat ive-Commutat ive deduction with constraints . . . . . . . . . . . . . . . . . . . . . . 530

Laurent Vigneron (CRIN-CNRS 8J INRIA Lorraine) AC-superposit ion with constraints: No AC-unifiers needed . . . . . . . . . . . . . . . . . 545

Robert Nieuwenhuis and Albert Rubio (Technical University of Catalonia) The complexity of counting problems in equational matching . . . . . . . . . . . . . . 560

Miki Hermann (CRIN ~ INRIA Lorraine) and Phokion G. Kolaitis (University of California at Santa Cruz)

H i g h e r - o r d e r t h e o r e m p r o v i n g

Representing proof t ransformations for program optimization . . . . . . . . . . . . . . 575 Penny Anderson (INRIA, Unitd de Recherche de Sophia-Antipolis)

Exploring abs t rac t algebra in constructive type theory . . . . . . . . . . . . . . . . . . . . . 590 Paul Jackson (Cornell University)

Tactic theorem proving with refinement-tree proofs and metavariables . . . . . 605 Amy Felty and Douglas Howe (AT~T Bell Laboratories)

H i g h e r - o r d e r u n i f i c a t i o n

Unification in an extensional lambda calculus with ordered function sorts and constant overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620

Patricia Johann and Michael Kohlhase (UniversitSt des Saarlandes) Decidable higher-order unification problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

Christian Prehofer ( Technische Universit?it Miinchen) Theory and practice of minimal modular higher-order E-unification . . . . . . . . 650

Olaf Miiller (Forschungszentrum Informatik) and Franz Weber (Bertelsmann Distribution)

G e n e r a l un i f i c a t i on A refined version of general E-unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

Roll Socher-Ambrosius (Max-Planck-Institut f'~r Informatik, Saarbr~cken)

A completion-based method for mixed universal and rigid E-unification . . . . 678 Bernhard Beckert (Universit?it Karlsruhe)

On pot, pans and pudding or how to discover generalised critical pairs . . . . . 693 Reinhard B~tndgen (UniversitSt Tiibingen)

N a t u r a l s y s t e m s

Semantic tableaux with ordering restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708 Stefan Klingenbeck and Reiner HShnle (University of Karlsruhe)

XIV

I n v i t e d t a l k Export ing and reflecting abst ract metamathemat ics . . . . . . . . . . . . . . . . . . . . . . . 529

Robert L. Constable (Cornell University)

A C u n i f i c a t i o n Associat ive-Commutat ive deduction with constraints . . . . . . . . . . . . . . . . . . . . . . 530

Laurent Vigneron (CRIN-CNRS 8J INRIA Lorraine) AC-superposit ion with constraints: No AC-unifiers needed . . . . . . . . . . . . . . . . . 545

Robert Nieuwenhuis and Albert Rubio (Technical University of Catalonia) The complexity of counting problems in equational matching . . . . . . . . . . . . . . 560

Miki Hermann (CRIN ~ INRIA Lorraine) and Phokion G. Kolaitis (University of California at Santa Cruz)

H i g h e r - o r d e r t h e o r e m p r o v i n g

Representing proof t ransformations for program optimization . . . . . . . . . . . . . . 575 Penny Anderson (INRIA, Unitd de Recherche de Sophia-Antipolis)

Exploring abs t rac t algebra in constructive type theory . . . . . . . . . . . . . . . . . . . . . 590 Paul Jackson (Cornell University)

Tactic theorem proving with refinement-tree proofs and metavariables . . . . . 605 Amy Felty and Douglas Howe (AT~T Bell Laboratories)

H i g h e r - o r d e r u n i f i c a t i o n

Unification in an extensional lambda calculus with ordered function sorts and constant overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620

Patricia Johann and Michael Kohlhase (UniversitSt des Saarlandes) Decidable higher-order unification problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

Christian Prehofer ( Technische Universit?it Miinchen) Theory and practice of minimal modular higher-order E-unification . . . . . . . . 650

Olaf Miiller (Forschungszentrum Informatik) and Franz Weber (Bertelsmann Distribution)

G e n e r a l un i f i c a t i on A refined version of general E-unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

Roll Socher-Ambrosius (Max-Planck-Institut f'~r Informatik, Saarbr~cken)

A completion-based method for mixed universal and rigid E-unification . . . . 678 Bernhard Beckert (Universit?it Karlsruhe)

On pot, pans and pudding or how to discover generalised critical pairs . . . . . 693 Reinhard B~tndgen (UniversitSt Tiibingen)

N a t u r a l s y s t e m s

Semantic tableaux with ordering restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708 Stefan Klingenbeck and Reiner HShnle (University of Karlsruhe)

XV

Strongly analytic tab leaux for normal modal logics . . . . . . . . . . . . . . . . . . . . . . . . 723 Fabio Massacci (Universitd di Roma "La Sapienza")

Reconstruct ing proofs at the assertion level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738 Xiaorong Huang (Universitdt des Saarlandes)

P r o b l e m se t s Problems on the generation of finite models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

Jian Zhang (Academia Sinica) Combining symbolic computa t ion and theorem proving: Some problems of Ramanujan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758

Edmund Clarke and Xudong Zhao (Carnegie Mellon University)

S y s t e m descriptions SCOTT: Semantically constrained O T T E R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764

John Slaney (The Australian National University), Ewing Lusk and William W. McCune (Argonne National Laboratory)

PROTEIN: A PROver with a Theory Extension INterface . . . . . . . . . . . . . . . . 769 Peter Baumgartner and Ulrich Furbach (Universitdt Koblenz)

DELTA - - A bo t tom-up preprocessor for top-down theorem provers . . . . . . . 774 Johann M. Ph. Schumann (Technische Universitdt Miinchen)

SETHEO V3.2: Recent developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778 Ch. Goller, R. Letz, K. Mayr and Johann M. Ph. Schumann (Technische Universitdt Miinchen)

KoMeT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783 W. Bibel, Stefan Briining~ U. Egly and T. Rath (Technische Hochschule Darmstadt)

~ - M K R P : A proof development environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 788 Xiaorong Huang, Manfred Kerber~ Michael Kohlhase, Erica Melis, Dan Nesmith, Jdrn Richts and Jdrg Siekmann (Universitdt des Saarlandes)

l e anTAp: Lean tableau-based theorem proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793 Bernhard Beckert and Joachim Posegga (Universitdt Karlsruhe)

FINDER: Fini te domain enumerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798 John Slaney (The Australian National University)

Symlog: Au toma ted advice in Fitch-style proof construction . . . . . . . . . . . . . . . . 802 Frederic D. Portoraro (University of Toronto)

KEIM: A toolkit for au tomated deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 Xiaorong Huang, Manfred Kerber, Michael Kohlhase, Erica Melis, Dan Nesmith, Jdrn Richts and Jdrg Siekmann (Universitdt des Saarlandes)

Elf: A meta- language for deductive systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 Frank P]enning (Carnegie Mellon University)

EUODHILOS-I I on top of GNU Epoch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816 Takeshi Ohtani, Hajime Sawamura and Toshiro Minami (Fujitsu Laboratories Ltd.)

xvI

Pi: An interactive derivation editor for the calculus of partial inductive definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821

Lars-Henrik Eriksson (Swedish Institute of Computer Science) Mollusc: A general proof-development shell for sequent-based logics . . . . . . . . 826

Bradley L. Riehards (Swiss Federal Institute of Technology), Ina Kraan (University of Zurich), Alan Smaill and Geraint A. Wiggins (University of Edinburgh)

KITP-93: An au tomated inference system for program analysis . . . . . . . . . . . . 831 T.C. Wang and Allen Goldberg (Kestrel Institute)

SPIKE: A system for sufficient completeness and parameterized inductive proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836

Adel Bouhoula (CRIN ~ INRIA Lorraine) Distributed theorem proving by Peers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841

Maria Paola Bonacina (University of Iowa) and William W. McCune (Argonne National Laboratory)

Author index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847