\begin{thebibliography}{}

\bibitem[\protect\citeauthoryear{Abrahams \bgroup \em et al.\egroup
  }{1980}]{seventhPOPLeighty}
Paul~W. Abrahams, Richard~J. Lipton, and Stephen~R. Bourne, editors.
\newblock {\em Conference Record of the \nth 7\,\POPLname, Las Vegas (NV),
  1980}. \acmpress, 1980.
\newblock \url{http://dl.acm.org/citation.cfm?id=567446}.

\bibitem[\protect\citeauthoryear{Acerbi{\protect\acerbiindex}}{2000}]{plato-in%
duction}
Fabio Acerbi{\protect\acerbiindex}.
\newblock {\plato: Parmenides 149a7--c3\@. A} proof by complete induction?
\newblock {\em Archive for History of Exact Sciences}, 55:57--76, 2000.

\bibitem[\protect\citeauthoryear{Ackermann\protect\ackermannindex}{1928}]{acke%
rmann-1928a}
Wilhelm Ackermann\protect\ackermannindex.
\newblock {Zum \hilbert schen Au\fbi au der reellen Zahlen}.
\newblock {\em {\MathematischeAnnalen}}, 99:118--133, 1928.
\newblock Received \Jan\,20, 1927.

\bibitem[\protect\citeauthoryear{Ackermann\protect\ackermannindex}{1940}]{acke%
rmann-consistency-of-arithmetic}
Wilhelm Ackermann\protect\ackermannindex.
\newblock {Zur Wider\-spruch\esi frei\-heit der Zahlen\-theorie}.
\newblock {\em {\MathematischeAnnalen}}, 117:163--194, 1940.
\newblock Received \Aug\,15, 1939.

\bibitem[\protect\citeauthoryear{A{\"\i}t-Kaci and Nivat}{1989}]{kaci-nivat}
Hassan A{\"\i}t-Kaci and Maurice Nivat, editors.
\newblock {\em {\Proc\ of the Colloquium on Resolution of Equations in
  Algebraic Structures (CREAS), Lakeway (TX), 1987}}. \academicpress, 1989.

\bibitem[\protect\citeauthoryear{Anon}{2005}]{aamp7g-2005}
Anon.
\newblock {Advanced Architecture MicroProcessor 7 Government (AAMP7G)}
  microprocessor.
\newblock Rockwell Collins, Inc. \WWW\ only:
  \url{http://www.rockwellcollins.com/sitecore/content/Data/Products/Informati%
on_Assurance/Cryptography/AAMP7G_Microprocessor.aspx}, 2005.

\bibitem[\protect\citeauthoryear{Armando \bgroup \em et al.\egroup
  }{2008}]{fourthIJCAReight}
Alessandro Armando, Peter Baumgartner, and Gilles Dowek, editors.
\newblock {\em {\thefourthIJCAReight}}, number 5195 in Lecture Notes in
  Artificial Intelligence. \springerverlag, 2008.

\bibitem[\protect\citeauthoryear{Aubin{\protectedaubinindex}}{1976}]{aubin-197%
6}
Raymond Aubin{\protectedaubinindex}.
\newblock {\em Mechanizing Structural Induction}.
\newblock PhD thesis, \uniEBshort, 1976.
\newblock Short version is \cite{aubin-1979}.
  \url{http://hdl.handle.net/1842/6649}.

\bibitem[\protect\citeauthoryear{Aubin{\protectedaubinindex}}{1979}]{aubin-197%
9}
Raymond Aubin{\protectedaubinindex}.
\newblock {Mechanizing Structural Induction --- Part\,I: Formal System.
  Part\,II: Strategies}.
\newblock {\em \tcsname}, 9:329--345+347--362, 1979.
\newblock Received March (Part\,I) and November (Part\,II) 1977, \rev\
  \Mar\,1978. Long version is \cite{aubin-1976}.

\bibitem[\protect\citeauthoryear{Autexier{\protectedautexierindex} \bgroup \em
  et al.\egroup }{1999}]{inkafuenf}
Serge Autexier{\protectedautexierindex}, Dieter Hutter{\protectedhutterindex},
  Heiko Mantel, and Axel Schairer.
\newblock System description: {\INKA\,5.0} -- a logical voyager.
\newblock 1999.
\newblock In \cite[\PP{207}{211}]{sixteenthCADEninetynine}.

\bibitem[\protect\citeauthoryear{Autexier{\protectedautexierindex}}{2005}]{ser%
getableau}
Serge Autexier{\protectedautexierindex}.
\newblock On the dynamic increase of multiplicities in matrix proof methods for
  classical higher-order logic.
\newblock 2005.
\newblock In \cite[\PP{48}{62}]{fourteenthTABLEAUfive}.

\bibitem[\protect\citeauthoryear{Avenhaus \bgroup \em et al.\egroup
  }{2003}]{quodlibet-cade}
J{\"u}rgen Avenhaus, Ulrich K{\"u}hler{\protectedkuehlerindex}, Tobias
  Schmidt-Samoa{\protectedsamoaindex}, and Claus-Peter
  Wirth{\protectedwirthindex}.
\newblock How to prove inductive theorems? {\QUODLIBET}!
\newblock 2003.
\newblock In \cite[\PP{328}{333}]{nineteenthCADEthree}, \www\url{/p/quodlibet}.

\bibitem[\protect\citeauthoryear{Baader}{2003}]{nineteenthCADEthree}
Franz Baader, editor.
\newblock {\em {\thenineteenthCADEthree}}, number 2741 in Lecture Notes in
  Artificial Intelligence. \springerverlag, 2003.

\bibitem[\protect\citeauthoryear{Baaz and Leitsch}{1995}]{baazleitschcolllog}
Matthias Baaz and Alexander Leitsch.
\newblock Methods of functional extension.
\newblock {\em Collegium Logicum --- Annals of the {\goedelname\ Society}},
  1:87--122, 1995.

\bibitem[\protect\citeauthoryear{Bachmair \bgroup \em et al.\egroup
  }{1992}]{Hotz-Festschrift}
Leo Bachmair, Harald Ganzinger, and Wolfgang~J. Paul, editors.
\newblock {\em {Informatik -- Festschrift zum 60.\,Geburt\esi tag von
  {\namefont G\ue nter Hotz}}}.
\newblock \teubnerverlag, 1992.

\bibitem[\protect\citeauthoryear{Bachmair}{1988}]{bachmair}
Leo Bachmair.
\newblock Proof by consistency in equational theories.
\newblock 1988.
\newblock In \cite[\PP{228}{233}]{lics3}.

\bibitem[\protect\citeauthoryear{Bajscy}{1993}]{ijcai13}
Ruzena Bajscy, editor.
\newblock {\em {\Proc\ \nth{13} \IJCAIname\ (\IJCAI), Chambery (France)}}.
  \morgankaufmann, 1993.
\newblock \url{http://ijcai.org/Past%20Proceedings}.

\bibitem[\protect\citeauthoryear{Barendregt}{1981}]{lambda-calculus-1st}
Hen(dri)k~P. Barendregt.
\newblock {\em The Lambda Calculus --- Its Syntax and Semantics}.
\newblock Number 103 in Studies in Logic and the Foundations of Mathematics.
  \northholland, 1981.
\newblock \nth 1\,\edn\ (final\,\rev\,\edn\ is \cite{lambda-calculus-final}).

\bibitem[\protect\citeauthoryear{Barendregt}{2012}]{lambda-calculus-final}
Hen(dri)k~P. Barendregt.
\newblock {\em The Lambda Calculus --- Its Syntax and Semantics}.
\newblock Number~40 in Studies in Logic. \collegepublications, 2012.
\newblock \nth 6\,\rev\,\edn\ (\nth 1\,\edn\ is \cite{lambda-calculus-1st}).

\bibitem[\protect\citeauthoryear{Barner{\protectedbarnerindex}}{2001a}]{fermat%
slife-english-2}
Klaus Barner{\protectedbarnerindex}.
\newblock {\fermatname\ (1601?--1665) --- His life beside mathematics}.
\newblock {\em European Mathematical Society Newsletter},
  43\,(\Dec\,2001):12--16, 2001.
\newblock Long version in German is \cite{fermatslife}.
  \url{www.ems-ph.org/journals/newsletter/pdf/2001-12-42.pdf}.

\bibitem[\protect\citeauthoryear{Barner{\protectedbarnerindex}}{2001b}]{fermat%
slife}
Klaus Barner{\protectedbarnerindex}.
\newblock {Da\es\ Leben \fermat\es}.
\newblock {\em \dmvmitteilungenname}, 3/2001:12--26, 2001.
\newblock Extensions in \cite{fermat-birth-date}. Short versions in English are
  \makeaciteoftwo{fermatslife-english-1}{fermatslife-english-2}.

\bibitem[\protect\citeauthoryear{Barner{\protectedbarnerindex}}{2001c}]{fermat%
slife-english-1}
Klaus Barner{\protectedbarnerindex}.
\newblock How old did {\fermat} become?
\newblock {\em NTM Internationale Zeitschrift f\ue r Geschichte und Ethik der
  Naturwissenschaften, Technik und Medizin, Neue Serie, ISSN\,00366978},
  9:209--228, 2001.
\newblock Long version in German is \cite{fermatslife}. New results on the
  subject in \cite{fermat-birth-date}.

\bibitem[\protect\citeauthoryear{Barner{\protectedbarnerindex}}{2007}]{fermat-%
birth-date}
Klaus Barner{\protectedbarnerindex}.
\newblock {Neue\es\ zu \fermat\es\ Geburt\esi datum}.
\newblock {\em \dmvmitteilungenname}, 15:12--14, 2007.
\newblock \bibcrit{Further support for the results of
  \cite{fermatslife-english-1}, narrowing down \fermat's birth date from 1607/8
  to \Nov\,1607}.

\bibitem[\protect\citeauthoryear{Basin and Walsh}{1996}]{rippling-calculus}
David Basin and Toby Walsh.
\newblock A calculus for and termination of rippling.
\newblock {\em \jarname}, 16:147--180, 1996.

\bibitem[\protect\citeauthoryear{Becker}{1965}]{becker-griechische}
Oscar Becker, editor.
\newblock {\em {Zur Geschichte der griechischen Mathematik}}.
\newblock \wissenschaftlichebuchgesellschaftdarmstadt, 1965.

\bibitem[\protect\citeauthoryear{Beckert}{2005}]{fourteenthTABLEAUfive}
Bernhard Beckert, editor.
\newblock {\em {\thefourteenthTABLEAUfive}}, number 3702 in Lecture Notes in
  Artificial Intelligence. \springerverlag, 2005.

\bibitem[\protect\citeauthoryear{Bell and Thayer}{1976}]{waterfall}
Thomas~E. Bell and T.~A. Thayer.
\newblock Software requirements: Are they really a problem?
\newblock 1976.
\newblock In \cite[\PP{61}{68}]{secondICSEseventysix},
  \url{http://pdf.aminer.org/000/361/405/software_requirements_are_they_really%
_a_problem.pdf}.

\bibitem[\protect\citeauthoryear{Benz{\-}m{\ue}ller{\protectedbenzmuellerindex}
  \bgroup \em et al.\egroup }{2008}]{C26}
{\mbox{Ch}}ristoph Benz{\-}m{\ue}ller{\protectedbenzmuellerindex}, Frank
  Theiss, Lawrence~C. Paulson, and Arnaud Fietz{\-}ke.
\newblock {\LEOII} --- a cooperative automatic theorem prover for higher-order
  logic.
\newblock 2008.
\newblock In \cite[\PP{162}{170}]{fourthIJCAReight}.

\bibitem[\protect\citeauthoryear{Berka and Kreiser}{1973}]{logiktexte}
Karel Berka and Lothar Kreiser, editors.
\newblock {\em {Logik-Texte -- Kommentierte Au\esi wahl zur Geschichte der
  modernen Logik}}.
\newblock \akademieverlag, 1973.
\newblock \nth 2\,\rev\,\edn\ (\nth 1\,\edn\,1971; \nth
  4\,\rev\,\rev\,\edn\,1986).

\bibitem[\protect\citeauthoryear{Bevers and Lewi}{1990}]{bevers&lewi}
Eddy Bevers and Johan Lewi.
\newblock Proof by consistency in conditional equational theories.
\newblock \Tech\ Report CW 102, \Dept\ \Comp\ \Sci, K. U. Leuven, 1990.
\newblock \Rev\,\Jul\,1990. Short version in
  \cite[\PP{194}{205}]{secondCTRSninety}.

\bibitem[\protect\citeauthoryear{Bevier \bgroup \em et al.\egroup
  }{1989}]{cli-1989-1}
William~R. Bevier, Warren~A. Hunt{\protectedhuntindex}, J~Strother
  Moore{\protect\mooreindex}, and William~D. Young.
\newblock An approach to systems verification.
\newblock {\em \jarname}, 5:411--428, 1989.

\bibitem[\protect\citeauthoryear{Bevier}{1989}]{bevier-1989}
William~R. Bevier.
\newblock Kit and the short stack.
\newblock {\em \jarname}, 5:519--530, 1989.

\bibitem[\protect\citeauthoryear{Bibel and
  Kowalski{\protectedkowalskiindex}}{1980}]{fifthCADEeighty}
Wolfgang Bibel and Robert~A. Kowalski{\protectedkowalskiindex}, editors.
\newblock {\em {\thefifthCADEeighty}}, number~87 in Lecture Notes in Computer
  Science. \springerverlag, 1980.

\bibitem[\protect\citeauthoryear{Biundo \bgroup \em et al.\egroup
  }{1986}]{inka}
Susanne Biundo, Birgit Hummel, Dieter Hutter{\protectedhutterindex}, and
  {\mbox{Ch}}ristoph Walther{\protectedwaltherindex}.
\newblock The {\KA} inductive theorem proving system.
\newblock 1986.
\newblock In \cite[\PP{673}{675}]{eighthCADEeightysix}.

\bibitem[\protect\citeauthoryear{Bledsoe{\protect\bledsoeindex} and
  Loveland}{1984}]{after-25-years}
W.~W. Bledsoe{\protect\bledsoeindex} and Donald~W. Loveland, editors.
\newblock {\em Automated Theorem Proving: After 25 Years}.
\newblock Number~29 in Contemporary Mathematics. \AMSname, Providence (RI),
  1984.
\newblock \Proc\ of the Special Session on Automatic Theorem Proving,
  \nth{89}\,Annual Meeting of the \AMSname, Denver (CO), \Jan\,1983.

\bibitem[\protect\citeauthoryear{Bledsoe{\protect\bledsoeindex} \bgroup \em et
  al.\egroup }{1971}]{BBH72-short}
W.~W. Bledsoe{\protect\bledsoeindex}, Robert~S. Boyer{\protect\boyerindex}, and
  William~H. Henneman.
\newblock Computer proofs of limit theorems.
\newblock 1971.
\newblock In \cite[\PP{586}{600}]{ijcai2}. Long version is \cite{BBH72}.

\bibitem[\protect\citeauthoryear{Bledsoe{\protect\bledsoeindex} \bgroup \em et
  al.\egroup }{1972}]{BBH72}
W.~W. Bledsoe{\protect\bledsoeindex}, Robert~S. Boyer{\protect\boyerindex}, and
  William~H. Henneman.
\newblock Computer proofs of limit theorems.
\newblock {\em \artificialintelligencename}, 3:27--60, 1972.
\newblock Short version is \cite{BBH72-short}.

\bibitem[\protect\citeauthoryear{Bledsoe{\protect\bledsoeindex}}{1971}]{Ble71}
W.~W. Bledsoe{\protect\bledsoeindex}.
\newblock Splitting and reduction heuristics in automatic theorem proving.
\newblock {\em \artificialintelligencename}, 2:55--77, 1971.

\bibitem[\protect\citeauthoryear{Bouajjani and
  Maler}{2009}]{twentyfirstCAVnine}
Ahmed Bouajjani and Oded Maler, editors.
\newblock {\em \Proc\ \nth{21} \Int\ \Conf\ on Computer Aided Verification
  (CAV), Grenoble (France), 2009}, volume 5643 of {\em Lecture Notes in
  Computer Science}. \springerverlag, 2009.

\bibitem[\protect\citeauthoryear{Bouhoula and Rusinowitch}{1995}]{spike}
Adel Bouhoula and Micha{\"e}l Rusinowitch.
\newblock Implicit induction in conditional theories.
\newblock {\em \jarname}, 14:189--235, 1995.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1939}]{bou%
rbaki-set-theory-results-1st-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Fascicule De R\'esultats}}.
\newblock Number 846 in \hermannparisseries. \hermannparis, 1939.
\newblock \nth 1\,\edn, \PPcount{VIII\,+\,50}. Review is \cite{churchbourbaki}.
  \nth 2 \rev\,\extd\,\edn\ is \cite{bourbaki-set-theory-results-2nd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1951}]{bou%
rbaki-set-theory-results-2nd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Fascicule De R\'esultats}}.
\newblock Number 846-1141 in \hermannparisseries. \hermannparis, 1951.
\newblock \nth 2\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-results-1st-edn}. \nth 3 \rev\,\extd\,\edn\ is
  \cite{bourbaki-set-theory-results-3rd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1954}]{bou%
rbaki-set-theory-chapter-1-2-1st-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,I\,\&\,II}}.
\newblock Number 1212 in \hermannparisseries. \hermannparis, 1954.
\newblock \nth 1\,\edn. \nth 2\,\rev\,\edn\ is
  \cite{bourbaki-set-theory-chapter-1-2-2nd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1956}]{bou%
rbaki-set-theory-chapter-3-1st-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,III}}.
\newblock Number 1243 in \hermannparisseries. \hermannparis, 1956.
\newblock \nth 1\,\edn,
  \PPcount{II\,+\,119\,+\,4\,(mode\,d'emploi)\,+\,23\,(errata\,{no.}\,6)}. \nth
  2\,\rev\,\extd\,\edn\ is \cite{bourbaki-set-theory-chapter-3-2nd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1958a}]{bo%
urbaki-set-theory-chapter-4-1st-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,IV}}.
\newblock Number 1258 in \hermannparisseries. \hermannparis, 1958.
\newblock \nth 1\,\edn. \nth 2\,\rev\,\extd\,\edn\ is
  \cite{bourbaki-set-theory-chapter-4-2nd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1958b}]{bo%
urbaki-set-theory-results-3rd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Fascicule De R\'esultats}}.
\newblock Number 1141 in \hermannparisseries. \hermannparis, 1958.
\newblock \nth 3\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-results-2nd-edn}. \nth 4 \rev\,\extd\,\edn\ is
  \cite{bourbaki-set-theory-results-4th-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1960}]{bou%
rbaki-set-theory-chapter-1-2-2nd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,I\,\&\,II}}.
\newblock Number 1212 in \hermannparisseries. \hermannparis, 1960.
\newblock \nth 2\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-chapter-1-2-1st-edn}. \nth 3\,\rev\,\edn\ is
  \cite{bourbaki-set-theory-chapter-1-2-3rd-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1964}]{bou%
rbaki-set-theory-results-4th-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Fascicule De R\'esultats}}.
\newblock Number 1141 in \hermannparisseries. \hermannparis, 1964.
\newblock \nth 4\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-results-3rd-edn}. \nth 5 \rev\,\extd\,\edn\ is
  \cite{bourbaki-set-theory-results-5th-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1966a}]{bo%
urbaki-set-theory-chapter-4-2nd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,IV}}.
\newblock Number 1258 in \hermannparisseries. \hermannparis, 1966.
\newblock \nth 2\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-chapter-4-1st-edn}. English translation in
  \cite{bourbaki-english}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1966b}]{bo%
urbaki-set-theory-chapter-1-2-3rd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitres\,I\,\&\,II}}.
\newblock Number 1212 in \hermannparisseries. \hermannparis, 1966.
\newblock \nth 3\,\rev\,\edn\,of
  \cite{bourbaki-set-theory-chapter-1-2-2nd-edn},
  \PPcount{VI\,+\,143\,+\,7\,(errata\,{no.}\,13)}. English translation in
  \cite{bourbaki-english}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1967}]{bou%
rbaki-set-theory-chapter-3-2nd-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Chapitre\,III}}.
\newblock Number 1243 in \hermannparisseries. \hermannparis, 1967.
\newblock \nth 2\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-chapter-3-1st-edn},
  \PPcount{151\,+\,7\,(errata\,{no.}\,13)}. \nth 3\,\rev\,\edn\ results from
  executing these errata. English translation in \cite{bourbaki-english}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1968a}]{bo%
urbaki-english}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em Elements of Mathematics --- Theory of Sets}.
\newblock \hermannparisseries. \hermannparis, jointly published with
  \mbox{AdiWes} International Series in Mathematics, \addisonwesley, 1968.
\newblock English translation of
  \makeaciteoffour{bourbaki-set-theory-chapter-1-2-3rd-edn}{bourbaki-set-theor%
y-chapter-3-2nd-edn}{bourbaki-set-theory-chapter-4-2nd-edn}{bourbaki-set-theor%
y-results-5th-edn}.

\bibitem[\protect\citeauthoryear{Bourbaki{\protectedbourbakiindex}}{1968b}]{bo%
urbaki-set-theory-results-5th-edn}
Nicola{\es} Bourbaki{\protectedbourbakiindex}.
\newblock {\em {\'El\'ements des Math\'ematique --- Livre\,1: Th\'eorie des
  Ensembles. Fascicule De R\'esultats}}.
\newblock Number 1141 in \hermannparisseries. \hermannparis, 1968.
\newblock \nth 5\,\rev\,\extd\,\edn\,of
  \cite{bourbaki-set-theory-results-4th-edn}. English translation in
  \cite{bourbaki-english}.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex} and
  Moore{\protect\mooreindex}}{1971}]{boyer-moore-1971}
Robert~S. Boyer{\protect\boyerindex} and J~Strother Moore{\protect\mooreindex}.
\newblock The sharing of structure in resolution programs.
\newblock Memo~47, \uniEBshort, \Dept\ of Computational Logic, 1971.
\newblock \PPcount{II\,+\,24}. Revised version is \cite{boyer-moore-1972}.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex} and
  Moore{\protect\mooreindex}}{1972}]{boyer-moore-1972}
Robert~S. Boyer{\protect\boyerindex} and J~Strother Moore{\protect\mooreindex}.
\newblock The sharing of structure in theorem-proving programs.
\newblock 1972.
\newblock In \cite[\PP{101}{116}]{machine-intelligence-7}.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex} and
  Moore{\protect\mooreindex}}{1973}]{boyer-moore-1973}
Robert~S. Boyer{\protect\boyerindex} and J~Strother Moore{\protect\mooreindex}.
\newblock Proving theorems about {LISP} functions.
\newblock 1973.
\newblock In \cite[\PP{486}{493}]{ijcai3}.
  \url{http://ijcai.org/Past%20Proceedings/IJCAI-73/PDF/053.pdf}. \Rev\
  version, \extd\ with a section ``Failures\closequotecomma is
  \cite{boyer-moore-1975}.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex} and
  Moore{\protect\mooreindex}}{1975}]{boyer-moore-1975}
Robert~S. Boyer{\protect\boyerindex} and J~Strother Moore{\protect\mooreindex}.
\newblock Proving theorems about {LISP} functions.
\newblock {\em {\jacmname}}, 22:129--144, 1975.
\newblock \Rev\,\extd\,\edn\,of \cite{boyer-moore-1973}. Received \Sep\,1973,
  \Rev\ \Apr\,1974.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex\bmfssapindex} and
  Moore{\protect\mooreindex}}{1977a}]{boyer-moore-fast-string-searching}
Robert~S. Boyer{\protect\boyerindex\bmfssapindex} and J~Strother
  Moore{\protect\mooreindex}.
\newblock A fast string searching algorithm.
\newblock {\em \commacmname}, 20:762--772, 1977.
\newblock \url{http://doi.acm.org/10.1145/359842.359859}.

\bibitem[\protect\citeauthoryear{Boyer{\protect\boyerindex} and
  Moore{\protect\mooreindex}}{1977b}]{boyer-moore-1977}
Robert~S. Boyer{\protect\boyerindex} and J~Strother Moore{\protect\mooreindex}.
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\bibitem[\protect\citeauthoryear{Voronkov}{1992}]{thirdLPARninetytwo}
Andrei Voronkov, editor.
\newblock {\em \Proc\ \nth 3 \LPARname\ (\LPAR)}, number 624 in Lecture Notes
  in Artificial Intelligence. \springerverlag, 1992.

\bibitem[\protect\citeauthoryear{Voronkov}{2002}]{eightteenthCADEtwo}
Andrei Voronkov, editor.
\newblock {\em {\theeightteenthCADEtwo}}, number 2392 in Lecture Notes in
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\bibitem[\protect\citeauthoryear{Walther{\protectedwaltherindex}}{1988}]{walth%
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{\mbox{Ch}}ristoph Walther{\protectedwaltherindex}.
\newblock Argument-bounded algorithms as a basis for automated termination
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\newblock 1988.
\newblock In \cite[\PP{601}{622}]{ninthCADEeightyeight}.

\bibitem[\protect\citeauthoryear{Walther{\protectedwaltherindex}}{1992}]{walth%
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\newblock Computing induction axioms.
\newblock 1992.
\newblock In \cite[\PP{381}{392}]{thirdLPARninetytwo}.

\bibitem[\protect\citeauthoryear{Walther{\protectedwaltherindex}}{1993}]{walth%
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{\mbox{Ch}}ristoph Walther{\protectedwaltherindex}.
\newblock Combining induction axioms by machine.
\newblock 1993.
\newblock In \cite[\PP{95}{101}]{ijcai13}.

\bibitem[\protect\citeauthoryear{Walther{\protectedwaltherindex}}{1994a}]{walt%
herhandbook}
{\mbox{Ch}}ristoph Walther{\protectedwaltherindex}.
\newblock Mathematical induction.
\newblock 1994.
\newblock In \cite[\PP{127}{228}]{handbooklogicailpvol2}.

\bibitem[\protect\citeauthoryear{Walther{\protectedwaltherindex}}{1994b}]{walt%
hertermination2}
{\mbox{Ch}}ristoph Walther{\protectedwaltherindex}.
\newblock On proving termination of algorithms by machine.
\newblock {\em \artificialintelligencename}, 71:101--157, 1994.

\bibitem[\protect\citeauthoryear{Wirsing and Nivat}{1996}]{fifthAMASTninetysix}
Martin Wirsing and Maurice Nivat, editors.
\newblock {\em \Proc\ \nth 5 \Int\ \Conf\ on Algebraic Methodology and Software
  Technology (AMAST), \Muenchen\ (Germany), 1996}, number 1101 in Lecture Notes
  in Computer Science. \springerverlag, 1996.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} and
  Becker}{1995}]{wirthbecker}
Claus-Peter Wirth{\protectedwirthindex} and Klaus Becker.
\newblock Abstract notions and inference systems for proofs by mathematical
  induction.
\newblock 1995.
\newblock In \cite[\PP{353}{373}]{fourthCTRSninetyfour}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} and
  Gram{\-}li{\protectedgramlichindex}ch}{1994a}]{wgjsc}
Claus-Peter Wirth{\protectedwirthindex} and Bernhard
  Gram{\-}li{\protectedgramlichindex}ch.
\newblock A constructor-based approach to positive/negative-conditional
  equational specifications.
\newblock {\em {\jscname}}, 17:51--90, 1994.
\newblock \url{http://dx.doi.org/10.1006/jsco.1994.1004}, \www\url{/p/jsc94}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} and
  Gram{\-}li{\protectedgramlichindex}ch}{1994b}]{wgcade}
Claus-Peter Wirth{\protectedwirthindex} and Bernhard
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\newblock On notions of inductive validity for first-order equational clauses.
\newblock 1994.
\newblock In \cite[\PP{162}{176}]{twelvethCADEninetyfour}, \www\url{/p/cade94}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} and
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Claus-Peter Wirth{\protectedwirthindex} and Ulrich
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\newblock {\em Inductive Theorem Proving in Theories Specified by \PNC\
  Equations}.
\newblock {SEKI-Report SR--95--15 (ISSN 1437--4447)}. {SEKI Publications},
  Univ.\ Kaiserslautern, 1995.
\newblock \PPcount{iv+126}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} \bgroup \em et
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Claus-Peter Wirth{\protectedwirthindex}, Bernhard
  Gram{\-}li{\protectedgramlichindex}ch, Ulrich
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\newblock {\em Constructor-Based Inductive Validity in
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\newblock {SEKI-Report SR--93--05~(SFB) (ISSN 1437--4447)}. {SEKI
  Publications}, \FBinfshort, \uniKLshort, 1993.
\newblock \PPcount{iv+58}, \urlsrninetythreedashzerofive. \Rev\,\extd\,\edn\ of
  \nth 1\,part is \cite{wgjsc}, \rev\,\edn\ of \nth 2\,part is \cite{wgcade}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex} \bgroup \em et
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Claus-Peter Wirth{\protectedwirthindex}, J{\"o}rg Siek{\-}mann,
  {\mbox{Ch}}ristoph Benz{\-}m{\ue}ller{\protectedbenzmuellerindex}, and Serge
  Autexier{\protectedautexierindex}.
\newblock \herbrandname: Life, logic, and automated deduction.
\newblock 2009.
\newblock In \cite[\Vol\,5: Logic from \russell\ to \church,
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\bibitem[\protect\citeauthoryear{Wirth}{1971}]{wirth-pascal}
Niklaus Wirth.
\newblock The programming language {\Pascal}.
\newblock {\em Acta Informatica}, 1:35--63, 1971.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{1991}]{wirth-mas%
ter}
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\newblock Inductive theorem proving in theories specified by
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\newblock \Diplomarbeit, \FBinfshort, \uniKLshort, 1991.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{1997}]{wirthdiss}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em Positive/Negative-Conditional Equations: A Constructor-Based
  Framework for Specification and Inductive Theorem Proving}, volume~31 of {\em
  {Schriftenreihe Forschungsergebnisse zur Informatik}}.
\newblock {Verlag Dr.\ Kova\v c, Hamburg}, 1997.
\newblock \PhDthesis, \uniKLshort, {ISBN 386064551X}, {\www\url{/p/diss}}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2004}]{wirthcard%
inal}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\DescenteInfinie\ + Deduction}.
\newblock {\em {\ljigplname}}, 12:1--96, 2004.
\newblock \www\url{/p/d}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2005a}]{zombie}
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\newblock History and future of implicit and inductionless induction: Beware
  the old jade and the zombie!
\newblock 2005.
\newblock In \cite[\PP{192}{203}]{siekmann-60}, {\www\url{/p/zombie}}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2005b}]{wirthcon%
fluence}
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\newblock {\em Syntactic Confluence Criteria for Positive/Negative-Conditional
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\newblock {SEKI-Report SR--95--09 (ISSN 1437--4447)}. {SEKI Publications},
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\newblock \Rev\,\edn\ \Oct\,2005 (\nth 1\,\edn\,1995), \PPcount{ii+188},
  \url{http://arxiv.org/abs/0902.3614}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2006}]{nonpermut}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em {$\lim$$+$}, {$\delta^+$}, and Non-Permutability of
  {$\beta$}-Steps}.
\newblock {SEKI-Report SR--2005--01 (ISSN 1437--4447)}. {SEKI Publications},
  Saarland Univ., 2006.
\newblock \Rev\,\edn\ \Jul\,2006 (\nth 1\,\edn\,2005), \PPcount{ii+36},
  \url{http://arxiv.org/abs/0902.3635}. Thoroughly improved version is
  \cite{wirth-jsc-non-permut}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2009}]{wirth-jsc}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock Shallow confluence of conditional term rewriting systems.
\newblock {\em {\jscname}}, 44:69--98, 2009.
\newblock \url{http://dx.doi.org/10.1016/j.jsc.2008.05.005}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2010a}]{swp20060%
1}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em Progress in Computer-Assisted Inductive Theorem Proving by
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\newblock {SEKI-Working-Paper SWP--2006--01 (ISSN 1860--5931)}. {SEKI
  Publications}, Saarland Univ., 2010.
\newblock \Rev\,\edn\,Dec\,2010 (\nth 1\,\edn\,2006), \PPcount{ii+36},
  \url{http://arxiv.org/abs/0902.3294}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2010b}]{fermatsp%
roof}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em A Self-Contained and Easily Accessible Discussion of the Method
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  Descente Infinie}}.
\newblock {SEKI-Working-Paper SWP--2006--02 (ISSN 1860--5931)}. {SEKI
  Publications}, {DFKI Bremen GmbH, Safe and Secure Cognitive Systems,
  Cartesium, Enrique Schmidt Str.\,5, D--28359 Bremen, Germany}, 2010.
\newblock \Rev\,\ed\,\Dec\,2010, \PPcount{ii+36},
  \url{http://arxiv.org/abs/0902.3623}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2012a}]{wirth-he%
ijenoort}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\herbrandsfundamentaltheorem} in the eyes of {\heijenoortname}.
\newblock {\em {\logicauniversalisname}}, 6:485--520, 2012.
\newblock Received \Jan\,12, 2012. Published online \Jun\,22, 2012,
  \url{http://dx.doi.org/10.1007/s11787-012-0056-7}.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2012b}]{wirth-js%
c-non-permut}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\math{\lim\tight+}, \math{\delta^+}, and \NonPermutability\ of
  \math\beta-Steps}.
\newblock {\em {\jscname}}, 47:1109--1135, 2012.
\newblock Received \Jan\,18, 2011. Published online \Jul\,15, 2011,
  \url{http://dx.doi.org/10.1016/j.jsc.2011.12.035}. More funny version is
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\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2012c}]{wirth-ma%
nifesto-ljigpl}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock Human-oriented inductive theorem proving by descente infinie --- {a
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\newblock {\em {\ljigplname}}, 20:1046--1063, 2012.
\newblock Received \Jul\,11, 2011. Published online \Mar\,12, 2012,
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\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2012d}]{boyer-mo%
ore-2012}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {Unpublished Interview of \boyername\ and \moorename\ at \boyer's
  place in Austin (TX) on Thursday, \Oct\,7}.
\newblock 2012.

\bibitem[\protect\citeauthoryear{Wirth{\protectedwirthindex}}{2013}]{SR--2011-%
-01}
Claus-Peter Wirth{\protectedwirthindex}.
\newblock {\em {A Simplified and Improved Free-Variable Framework for
  \hilbert's epsilon as an Operator of Indefinite Committed Choice}}.
\newblock {SEKI Report SR--2011--01 (ISSN 1437--4447)}. {SEKI Publications},
  {DFKI Bremen GmbH, Safe and Secure Cognitive Systems, Cartesium, Enrique
  Schmidt Str.\,5, D--28359 Bremen, Germany}, 2013.
\newblock \Rev\,\edn\ \Jan\,2013 (\nth 1\,\edn\,2011), \PPcount{ii+65},
  {\url{http://arxiv.org/abs/1104.2444}}.

\bibitem[\protect\citeauthoryear{Wolff}{1728}]{wolff-rationalis}
Christian Wolff.
\newblock {\em Philosophia rationalis sive Logica, methodo scientifica
  pertractata et ad usum scientiarium atque vitae aptata}.
\newblock Rengerische Buchhandlung, \FFM\ \& \Leipzig, 1728.
\newblock \nth 1\,\edn.

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Christian Wolff.
\newblock {\em Philosophia rationalis sive Logica, methodo scientifica
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\newblock Rengerische Buchhandlung, \FFM\ \& \Leipzig, 1740.
\newblock \nth 3\,\extd\,\edn\ of \cite{wolff-rationalis}\@. \ Facsimile
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Raymond~T. Yeh and C.~V. Ramamoorthy, editors.
\newblock {\em \Proc\ \nth 2 \Int\ \Conf\ on Software Engineering, San
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\newblock \url{http://dl.acm.org/citation.cfm?id=800253}.

\bibitem[\protect\citeauthoryear{Young}{1989}]{young-1989}
William~D. Young.
\newblock A mechanically verified code generator.
\newblock {\em \jarname}, 5:493--518, 1989.

\bibitem[\protect\citeauthoryear{Zhang \bgroup \em et al.\egroup
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Han{\-}tao Zhang, Deepak Kapur, and Mukkai~S. Krishnamoorthy.
\newblock A mechanizable induction principle for equational specifications.
\newblock 1988.
\newblock In \cite[\PP{162}{181}]{ninthCADEeightyeight}.

\bibitem[\protect\citeauthoryear{Zygmunt}{1991}]{presburger-life}
Jan Zygmunt.
\newblock \presburgername: Life and work.
\newblock {\em History and Philosophy of Logic}, 12:211--223, 1991.

\end{thebibliography}
