\relax \bibstyle{named} \citation{vampire01} \citation{waldmeister} \citation{HL02} \citation{chaff} \citation{C26} \citation{satallax} \newlabel{1-fp}{{1}{1}} \@writefile{toc}{\contentsline {Chapter}{{\unhbox \voidb@x \hbox {\MakeTextUppercase {{{J\nobreakspace {}Strother {Moore}}, {Clau\unprotectedes -Peter\ {Wirth}}}}}\\ {{Automation\nobreakspace {}of Mathematical\nobreakspace {}Induction as\nobreakspace {}part\nobreakspace {}of\nobreakspace {}the\nobreakspace {}History\nobreakspace {}of\nobreakspace {}Logic}}}}{1}} \@writefile{toc}{\contentsline {section}{\numberline {1}\MakeTextUppercase {A Snapshot of a Decisive Moment in History}}{1}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {1}A Snapshot of a Decisive Moment in History}{1}} \newlabel{section Preface}{{1}{1}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The {Boyer}--{Moore}\ Waterfall}}{1}} \newlabel{figure waterfall}{{1}{1}} \newlabel{note higher-order theorem provers}{{3}{1}} \citation{waterfall} \citation{bm} \citation{moore-1973} \citation{boyer-moore-1973} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces {Ro\discretionary {-}{}{}bert\ S. {Boyer}}\ (1971) (l.)\ and {J\nobreakspace {}Strother {Moore}}\ (1972?) (r.)}}{2}} \citation{meltzer-1975} \citation{kowalski-1988} \newlabel{note people and departments}{{7}{3}} \citation{boyer-moore-1971} \citation{moore-1973} \citation{moore-1973} \citation{Kow74} \citation{Kow74} \citation{kowalski-1988} \citation{Prolog} \citation{pop2} \citation{boyer-moore-davies-1973} \citation{moore-1981} \citation{simonyi-interview} \citation{waltherhandbook} \citation{bundy-survey} \@writefile{toc}{\contentsline {section}{\numberline {2}\MakeTextUppercase {Method of Procedure and Presentation}}{5}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {2}Method of Procedure and Presentation}{5}} \citation{LISP} \citation{boyer-moore-1973} \citation{moore-1973} \citation{haskell} \citation{Pau96} \citation{scott-LCF} \citation{scott-LCF} \citation{milner-1972} \citation{fromLCFtoHOL} \citation{wgjsc} \citation{wirth-master} \citation{wirth-master} \citation{wirth-jsc} \citation{term-rewriting-one} \citation{wgjsc} \citation{wirth-master} \citation{wirth-master} \citation{wirth-jsc} \citation{KB70} \citation{huet} \citation{toyama} \citation{firstCTRSeightyseven} \citation{wirth-jsc} \citation{bm} \citation{moore-1973} \citation{bm} \citation{bm} \citation{boyermoore} \citation{boyermooresecondedition} \citation{waltherhandbook} \citation{bundy-survey} \citation{ACLTWO-CASESTUDIES} \citation{ACLTWO-CASESTUDIES} \citation{ACLTWO} \@writefile{toc}{\contentsline {section}{\numberline {3}\MakeTextUppercase {Organization of this Article}}{8}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {3}Organization of this Article}{8}} \citation{cajori-1918} \citation{hippa} \citation{plato-induction} \citation{elements} \citation{freudenthal} \citation{unguru-one} \citation{plato-induction} \citation{Greeks-induction} \citation{fermatsproof} \citation{Ravinovitch-Gershon} \citation{katz-history} \citation{maurolycus} \citation{pascal} \@writefile{toc}{\contentsline {section}{\numberline {4}\MakeTextUppercase {Mathematical Induction}}{9}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {4}Mathematical Induction}{9}} \newlabel{section What is mathematical induction?}{{4}{9}} \citation{fermat-birth-date} \citation{catherine-goldstein-fermat-priceton-companion-math-2008} \citation{fermatsproof} \citation{wirthcardinal} \citation{wirthcardinal} \citation{axiomofchoice} \citation{weakaxiomofchoice} \@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Well-Founded\discretionary {-}{}{}ness\ and Termination}{10}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.1}Well-Founded\discretionary {-}{}{}ness\ and Termination}{10}} \newlabel{subsection Well-Foundedness and Termination}{{4.1}{10}} \newlabel{lemma 1}{{1}{10}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.2}The Theorem of\/ {Noether}\discretionary {-}{}{}ian\ Induction}{10}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.2}The Theorem of\/ {Noether}\discretionary {-}{}{}ian\ Induction}{10}} \newlabel{subsection noetherian induction}{{4.2}{10}} \citation{cohn-1965} \citation{bourbaki-english} \citation{bourbaki-set-theory-chapter-3-2nd-edn} \citation{schoenfield} \citation{bourbaki-set-theory-chapter-3-1st-edn} \citation{bourbaki-set-theory-chapter-3-2nd-edn} \citation{bourbaki-set-theory-chapter-3-1st-edn} \citation{bourbaki-set-theory-chapter-3-2nd-edn} \citation{geseraxiomofchoice} \@writefile{toc}{\contentsline {subsection}{\numberline {4.3}An Induction Principle Stronger than {Noether}\discretionary {-}{}{}ian\ Induction?}{11}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.3}An Induction Principle Stronger than {Noether}\discretionary {-}{}{}ian\ Induction?}{11}} \newlabel{subsection Beyond Noetherian induction}{{4.3}{11}} \newlabel{note complete induction}{{34}{11}} \citation{geseraxiomofchoice} \citation{axiomofchoice} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4}The Natural Numbers}{12}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.4}The Natural Numbers}{12}} \newlabel{subsection Mathematical Induction and the Natural Numbers}{{4.4}{12}} \citation{dedekind-1888} \citation{wolff-rationalis-1740} \citation{lambert-1764} \citation{fries-vollstaendige-induction} \citation{heijenoort-source-book} \citation{grundlagen-german-english-edition-volume-one-one} \citation{peter-1951} \citation{ackermann-1928a} \newlabel{note fries}{{38}{13}} \citation{wirthcardinal} \citation{pieri} \citation{pieri} \citation{peanonovamethodo} \citation{padoa-1913} \citation{smith-pieri} \citation{pieri} \citation{pieri} \newlabel{note pieri standard}{{42}{14}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.5}Standard Data Types}{15}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.5}Standard Data Types}{15}} \newlabel{subsection Standard Data Types}{{4.5}{15}} \citation{bm} \citation{wirthcardinal} \citation{grundlagen-second-edition-volume-two} \citation{gentzen} \citation{gwrta} \citation{wirth-jsc} \citation{grundlagen-second-edition-volume-two} \citation{ackermann-consistency-of-arithmetic} \@writefile{toc}{\contentsline {subsection}{\numberline {4.6}The Standard High-Level Method of Mathematical Induction}{18}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.6}The Standard High-Level Method of Mathematical Induction}{18}} \newlabel{subsection The Standard High-Level Method of Mathematical Induction}{{4.6}{18}} \newlabel{section items}{{4.6}{18}} \citation{fermat-oeuvres} \citation{fermat-career} \citation{From-Fermat-to-Gauss} \citation{fermatsproof} \citation{fermatsproof} \citation{fermat-oeuvres} \citation{wirthcardinal} \citation{DBLP:conf/lics/BrotherstonS07} \citation{DBLP:conf/lics/BrotherstonS07} \citation{brotherston-cut-elimination} \citation{voicu-li-di} \citation{zombie} \citation{zombie} \citation{swp200601} \citation{SR--2011--01} \citation{wirth-manifesto-ljigpl} \citation{From-Fermat-to-Gauss} \citation{fermatsproof} \@writefile{toc}{\contentsline {subsection}{\numberline {4.7}{\it Descente Infinie}}{19}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.7}{\it Descente Infinie}}{19}} \newlabel{subsection DescenteInfinie}{{4.7}{19}} \citation{sergetableau} \newlabel{section example first proof of (+3)}{{4.7}{20}} \newlabel{example first proof of (+3)}{{2}{20}} \newlabel{section example first proof of (less7)}{{4.7}{21}} \newlabel{example first proof of (less7)}{{3}{21}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.8}Explicit Induction}{22}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.8}Explicit Induction}{22}} \newlabel{subsection Explicit Induction}{{4.8}{22}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.8.1}From the Theorem of\/ {Noether}\discretionary {-}{}{}ian\ Induction\ to Explicit Induction}{22}} \newlabel{section example second proof of (+3)}{{4.8.1}{23}} \newlabel{example second proof of (+3)}{{4}{23}} \citation{waltherIJCAI93} \citation{wirthcardinal} \citation{church-rosser-bm} \citation{church-rosser-bm} \citation{lambda-calculus-final} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.8.2}Theoretical Viewpoint on Explicit Induction}{25}} \newlabel{subsubsection Theoretical Viewpoint}{{4.8.2}{25}} \newlabel{note Newman}{{64}{25}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {4.8.3}Practical Viewpoint on Explicit Induction}{26}} \newlabel{subsubsection Practical Viewpoint}{{4.8.3}{26}} \citation{aubin-1976} \@writefile{toc}{\contentsline {subsection}{\numberline {4.9}Generalization}{27}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.9}Generalization}{27}} \newlabel{subsection Generalization}{{4.9}{27}} \newlabel{section example proof of (ack4)}{{4.9}{27}} \citation{wirthcardinal} \newlabel{example proof of (ack4)}{{5}{28}} \citation{goedel} \citation{gentzen} \citation{induction-no-cut} \citation{baazleitschcolllog} \@writefile{toc}{\contentsline {subsection}{\numberline {4.10}Proof-Theoretical Peculiarities of Mathematical Induction}{29}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.10}Proof-Theoretical Peculiarities of Mathematical Induction}{29}} \newlabel{subsection Proof-Theoretical Peculiarities of Mathematical Induction}{{4.10}{29}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.11}Conclusion}{29}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {4.11}Conclusion}{29}} \newlabel{note practice one}{{72}{29}} \newlabel{note practice two}{{75}{29}} \citation{wirth-jsc} \@writefile{toc}{\contentsline {section}{\numberline {5}\MakeTextUppercase {Recursion, Termination, and Induction}}{30}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {5}Recursion, Termination, and Induction}{30}} \newlabel{section Recursive Definitions}{{5}{30}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Recursion and the Rewrite Relation on Ground Terms}{30}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.1}Recursion and the Rewrite Relation on Ground Terms}{30}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Confluence}{30}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.2}Confluence}{30}} \newlabel{subsection Confluence}{{5.2}{30}} \citation{bm} \citation{moore-1973} \citation{bm} \citation{LISP} \citation{bm} \newlabel{section example PLUS}{{5.2}{31}} \newlabel{example PLUS}{{6}{31}} \newlabel{note applicative}{{81}{31}} \citation{wirth-jsc} \citation{wirth-jsc} \citation{bm} \citation{wgcade} \citation{wirth-jsc} \citation{schoenfield} \citation{moore-1973} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Termination and Reducibility}{32}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.3}Termination and Reducibility}{32}} \newlabel{subsection Termination and Reducibility}{{5.3}{32}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Constructor Variables}{32}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.4}Constructor Variables}{32}} \newlabel{subsection Constructor Variables}{{5.4}{32}} \citation{moore-1973} \citation{wgkp} \citation{wgjsc} \citation{wgjsc} \citation{wgcade} \citation{kwspec} \citation{kwspec} \citation{kwspec2} \citation{wirthdiss} \citation{wirthdiss} \citation{wirth-jsc} \citation{kuehlerdiss} \citation{quodlibet-cade} \citation{samoacalculemus} \citation{samoacalculemus} \citation{samoa-phd} \citation{jancl} \citation{wgcade} \citation{kwspec2} \citation{moore-1973} \citation{bm} \citation{bm} \citation{waltherLPAR92} \citation{waltherLPAR92} \citation{waltherIJCAI93} \@writefile{toc}{\contentsline {subsection}{\numberline {5.5}Termination and General Induction Templates}{34}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.5}Termination and General Induction Templates}{34}} \newlabel{subsection Termination}{{5.5}{34}} \newlabel{note on IF and COND}{{89}{34}} \newlabel{example induction template two measured subsets constructor style}{{7}{35}} \newlabel{example non-singleton measured subset constructor style}{{8}{35}} \citation{wirthdiss} \citation{wirth-jsc} \citation{wirthdiss} \@writefile{toc}{\contentsline {subsection}{\numberline {5.6}Termination of the Rewrite Relation on Ground Terms}{36}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.6}Termination of the Rewrite Relation on Ground Terms}{36}} \newlabel{note on general variables}{{94}{36}} \citation{mutualexplicitinduction} \citation{bm} \@writefile{toc}{\contentsline {subsection}{\numberline {5.7}Applicable Induction Templates for Explicit Induction}{37}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.7}Applicable Induction Templates for Explicit Induction}{37}} \newlabel{section example Applicable Induction Templates constructor style}{{5.7}{38}} \newlabel{example Applicable Induction Templates constructor style}{{9}{38}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.8}Induction Schemes}{38}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {5.8}Induction Schemes}{38}} \newlabel{subsection Induction Schemes}{{5.8}{38}} \citation{bm} \citation{fitting} \citation{Fitting90} \citation{wirthcardinal} \citation{wirthcardinal} \citation{wirth-jsc-non-permut} \citation{SR--2011--01} \newlabel{section example induction schemes constructor style}{{5.8}{40}} \newlabel{example induction schemes constructor style}{{10}{40}} \citation{davis-2009} \@writefile{toc}{\contentsline {section}{\numberline {6}\MakeTextUppercase {Automated Explicit Induction}}{41}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {6}Automated Explicit Induction}{41}} \newlabel{section Explicit Induction}{{6}{41}} \@writefile{toc}{\contentsline {subsection}{\numberline {6.1}The Application Context of Automated Explicit Induction}{41}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.1}The Application Context of Automated Explicit Induction}{41}} \newlabel{subsection The Application Context of Automated Explicit Induction}{{6.1}{41}} \citation{burstall-1969} \citation{burstall-1969} \citation{darlington-1968} \citation{Ble71} \citation{Ble71} \citation{bm} \citation{boyer-moore-1973} \citation{moore-1973} \citation{moore-1975} \@writefile{toc}{\contentsline {subsection}{\numberline {6.2}The\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{42}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.2}The\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{42}} \newlabel{The Pure Lisp Theorem Prover}{{6.2}{42}} \newlabel{note burstall quotation}{{102}{42}} \citation{moore-1973} \citation{boyer-moore-2012} \citation{moore-1973} \citation{burstall-1969} \citation{BBH72} \citation{pop2} \citation{moore-1973} \citation{moore-1973} \citation{moore-1973} \citation{wirth-jsc} \citation{moore-1973} \citation{moore-1973} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.1}Simplification in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{45}} \newlabel{subsubsection Simplification in the pure}{{6.2.1}{45}} \citation{moore-1973} \citation{samoa-phd} \citation{samoa-phd} \citation{jancl} \newlabel{note no destructor elimination}{{119}{47}} \citation{moore-1973} \citation{moore-1973} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.2}Destructor Elimination in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{48}} \newlabel{subsubsection Destructor Elimination in the PURE}{{6.2.2}{48}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.3}(Cross-) Fertilization in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{48}} \newlabel{fertilization in pure lisp theorem prover}{{6.2.3}{48}} \citation{moore-1973} \citation{moore-1973} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.4}Generalization in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{49}} \newlabel{subsubsection Generalization pure lisp theorem prover}{{6.2.4}{49}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.5}Elimination of Irrelevance in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{49}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.6}Induction in the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{49}} \newlabel{subsubsection Induction of pure lisp theorem prover}{{6.2.6}{49}} \newlabel{note failure of synthesis}{{122}{49}} \citation{moore-1973} \newlabel{section example induction rule}{{6.2.6}{50}} \newlabel{example induction rule}{{11}{50}} \newlabel{section example merging}{{6.2.6}{51}} \newlabel{section example second proof of (less7)}{{6.2.6}{51}} \newlabel{example second proof of (less7)}{{12}{51}} \newlabel{example merging}{{12}{51}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.7}Conclusion on the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{51}} \newlabel{subsubsection Conclusion on the pure lisp theorem prover}{{6.2.7}{51}} \citation{moore-1973} \citation{bm} \citation{bm} \@writefile{toc}{\contentsline {subsection}{\numberline {6.3}{\sc Thm}}{52}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.3}{\sc Thm}}{52}} \newlabel{subsection theorem prover}{{6.3}{52}} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \citation{moore-1975} \citation{moore-1975} \citation{boyer-moore-1975} \citation{boyer-2012} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \citation{boyer-2012} \citation{boyermoore} \citation{bm} \citation{moore-1973} \citation{bm} \citation{boyermoore} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \citation{wirth-pascal} \citation{bm} \citation{bm} \citation{boyermoore} \citation{boyermooresecondedition} \newlabel{note jargon one}{{134}{54}} \citation{bm} \citation{boyermoore} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \citation{boyermoore} \citation{boyermoore} \citation{boyermooresecondedition} \newlabel{note PACK}{{135}{55}} \citation{bm} \citation{bm} \citation{bm} \citation{bm} \citation{bm} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.1}Simplification in\/ {\sc Thm}}{57}} \newlabel{subsubsection simplification in}{{6.3.1}{57}} \newlabel{note kaufmann non-standard}{{139}{57}} \citation{bm} \citation{bm} \citation{KB70} \citation{bm} \citation{jancl} \citation{bm} \citation{bm} \citation{boyermoore} \citation{boyermoore} \citation{boyermooresecondedition} \citation{bm} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.2}Destructor Elimination in\/ {\sc Thm}}{61}} \newlabel{subsubsection Destructor Elimination in}{{6.3.2}{61}} \newlabel{example and back}{{15}{61}} \citation{bm} \citation{bm} \newlabel{example d l once}{{16}{62}} \citation{bm} \newlabel{example quotient and remainder}{{17}{63}} \citation{bm} \citation{bm} \citation{bm} \citation{bm} \citation{bm} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.3}(Cross-) Fertilization in\/ {\sc Thm}}{65}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.4}Generalization in\/ {\sc Thm}}{65}} \citation{bm} \citation{wirthcardinal} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.5}Elimination of Irrelevance in\/ {\sc Thm}}{66}} \newlabel{subsubsection Elimination of Irrelevance in}{{6.3.5}{66}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.6}Induction in\/ {\sc Thm}\ as compared to the\/ {\sc Pure {\sc LISP}\ Theo\discretionary {-}{}{}rem Pro\discretionary {-}{}{}ver}}{67}} \newlabel{subsubsection Induction in}{{6.3.6}{67}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.7}Induction Templates generated by Definition-Time Recursion Analysis}{67}} \newlabel{subsubsection Induction Templates}{{6.3.7}{67}} \citation{bm} \citation{bm} \citation{bm} \newlabel{section example induction template two measured subsets}{{6.3.7}{68}} \newlabel{example induction template two measured subsets}{{18}{68}} \newlabel{example non-singleton measured subset}{{19}{68}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.8}Proof-Time Recursion Analysis in\/ {\sc Thm}}{69}} \newlabel{subsubsection Proof-Time Recursion Analysis in}{{6.3.8}{69}} \newlabel{example Applicable Induction Templates}{{20}{69}} \newlabel{example induction schemes}{{21}{69}} \citation{bm} \newlabel{example Subsumption}{{22}{70}} \newlabel{note injectivity 1}{{168}{70}} \newlabel{section example merging 2}{{6.3.8}{71}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \footroom The induction schemes of Ex\discretionary {-}{}{}am\discretionary {-}{}{}ple\,23\hbox {}}}{71}} \newlabel{figure induction schemes}{{3}{71}} \citation{bm} \citation{bm} \citation{bm} \newlabel{example merging 2}{{23}{72}} \newlabel{note injectivity 2}{{169}{72}} \citation{waltherLPAR92} \citation{waltherLPAR92} \citation{waltherIJCAI93} \citation{stevens-rational-reconstruction} \citation{bundy-recursion-analysis} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.3.9}Conclusion on {\sc Thm}}{73}} \newlabel{subsubsection Conclusion on}{{6.3.9}{73}} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Four possibilities to descend with rational representations of \nlbmath {\sqrt 2}:}}{74}} \newlabel{figure square root}{{4}{74}} \citation{bm} \citation{boyer-moore-1981-authors} \citation{bmeval-1988} \citation{boyermoore} \citation{boyermoore} \citation{boyermooresecondedition} \citation{presburger} \citation{presburger-remarks-translation} \citation{presburger-life} \citation{boyer-moore-1988} \@writefile{toc}{\contentsline {subsection}{\numberline {6.4}{\sc Nqthm}}{75}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.4}{\sc Nqthm}}{75}} \newlabel{subsection NQTHM}{{6.4}{75}} \newlabel{note presburger}{{175}{75}} \citation{hunt-1985} \citation{shankar-1994} \citation{shankar-1994} \citation{moore-1989-1} \citation{moore-1989-1} \citation{moore-1989-2} \citation{cli-1989-1} \citation{hunt-1989} \citation{young-1989} \citation{bevier-1989} \citation{c-string-lib-1996} \citation{boyermooresecondedition} \citation{boyermoore} \citation{commonlisp} \@writefile{toc}{\contentsline {subsection}{\numberline {6.5}{\sc ACL2}}{76}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.5}{\sc ACL2}}{76}} \newlabel{subsection ACLTWO}{{6.5}{76}} \newlabel{note shankar}{{176}{76}} \citation{boyermooresecondedition} \citation{ACLTWO} \citation{brock-hunt-1999} \citation{moore-lynch-kaufmann-1998} \citation{russinoff-1998} \citation{aamp7g-2005} \citation{hunt-swords-2009} \citation{brock-hunt-1999} \citation{moore-lynch-kaufmann-1998} \citation{rrl} \citation{walthertermination} \citation{walthertermination} \citation{walthertermination2} \citation{waltherLPAR92} \citation{waltherLPAR92} \citation{waltherIJCAI93} \citation{protzenlazy} \citation{protzenlazy} \citation{protzendiss} \citation{protzenpatching} \@writefile{toc}{\contentsline {subsection}{\numberline {6.6}Further Historically Important Explicit-Induction Systems}{78}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {6.6}Further Historically Important Explicit-Induction Systems}{78}} \newlabel{subsection Further Most Noteworthy Explicit-Induction Systems}{{6.6}{78}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.6.1}{\sc Rrl}}{78}} \newlabel{section RRL}{{6.6.1}{78}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.6.2}{\sc Inka}}{78}} \newlabel{section INKA}{{6.6.2}{78}} \citation{inkafuenf} \citation{inka} \citation{inkanext} \citation{inkafuenf} \citation{inductioncontest} \citation{bm} \citation{inkafuenf} \citation{bm} \citation{inka} \citation{inkanext} \citation{oysterclam} \citation{bundy-survey} \citation{nuprl-book} \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.6.3}{\sc Oyster}/{\rm CL\kern -.36em\raise .39ex\hbox {\sc a}\kern -.15emM}}{79}} \newlabel{note induction contest}{{180}{79}} \citation{failure-guide-induction} \citation{bundy-recursion-analysis} \citation{bundy-survey} \citation{science-of-reasoning} \citation{bundy-inductive-proof-planning} \citation{proofplanningsystems} \@writefile{toc}{\contentsline {section}{\numberline {7}\MakeTextUppercase {Alternative Approaches Besides Explicit Induction}}{80}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {7}Alternative Approaches Besides Explicit Induction}{80}} \newlabel{section Alternative Approaches to the Automation of Induction}{{7}{80}} \@writefile{toc}{\contentsline {subsection}{\numberline {7.1}Proof Planning}{80}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {7.1}Proof Planning}{80}} \newlabel{subsection Proof Planning}{{7.1}{80}} \citation{science-of-reasoning} \citation{science-of-reasoning} \citation{bundy-inductive-proof-planning} \citation{proofplanningsystems} \citation{dodi-diss} \citation{proof_planning_with_multiple_strategies} \citation{automatic-learning-proof-planning} \citation{aubin-1976} \citation{aubin-1976} \citation{aubin-1976} \citation{aubin-1976} \citation{aubin-1976} \citation{rippling-book} \citation{aubin-1976} \citation{aubin-1976} \citation{aubin-1979} \citation{rippling-book} \citation{hutter-rippling} \citation{rippling} \citation{failure-guide-induction} \citation{rippling-calculus} \citation{failure-guide-induction} \@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Rippling}{81}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {7.2}Rippling}{81}} \newlabel{subsection Rippling}{{7.2}{81}} \citation{bm} \citation{boyer-moore-1975} \citation{boyer-moore-1975} \citation{bm} \citation{huethullotinductionlessinduction} \citation{boyer-moore-1977} \citation{musserinductionlessinduction} \citation{inductionlessinduction1} \citation{inductionlessinduction1} \citation{gogueninductionlessinduction} \citation{gogueninductionlessinduction} \citation{aubin-1976} \citation{bm} \citation{bm} \citation{gogueninductionlessinduction} \citation{huethullotinductionlessinduction} \citation{inductionlessinduction1} \citation{musserinductionlessinduction} \citation{inductionlesshistc} \citation{inductionlesshista} \citation{inductionlesshistb} \citation{inductionlesshistd} \citation{bachmair} \citation{ZKK88} \citation{rrl} \citation{bevers&lewi} \citation{reddy} \citation{unicom} \citation{GaSt} \citation{spike} \citation{padawitzjsc} \citation{bachmair} \citation{bm} \citation{kapur1} \citation{kapur2} \citation{unicom} \citation{bachmair} \citation{KB70} \citation{GaSt} \@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Implicit Induction}{82}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {7.3}Implicit Induction}{82}} \citation{unicom} \citation{GaSt} \citation{bachmair} \citation{wirthdiss} \citation{kuehlerdiss} \citation{wirthbecker} \citation{bachmair} \citation{SR--88--12} \citation{SR--88--12} \citation{simplificationorderings} \citation{geser-improved-general-path-order} \citation{inductionlessinduction1} \citation{inductionlessinduction1} \citation{inductionlessinduction2} \citation{gogueninductionlessinduction} \citation{protzenlazy} \citation{comonAR} \citation{zombie} \citation{kuehler-master} \citation{unicom} \citation{kuehler-master} \citation{kuehler-master} \@writefile{toc}{\contentsline {subsection}{\numberline {7.4}{\sc Quod\discretionary {-}{}{}Libet}}{84}} \@writefile{ptc1}{\contentsline {Psubsection}{\numberline {7.4}{\sc Quod\discretionary {-}{}{}Libet}}{84}} \newlabel{section QUODLIBET}{{7.4}{84}} \citation{loechner-lpo} \citation{wirthdiss} \citation{kuehlerdiss} \citation{wirth-master} \citation{wgjsc} \citation{wgkp} \citation{wgcade} \citation{wirth-jsc} \citation{kwspec} \citation{kwspec} \citation{wirthconfluence} \citation{wgcade} \citation{kwspec} \citation{loechner-lpo} \citation{quodlibet-cade} \citation{SR--95--15} \citation{wirthdiss} \citation{kuehlerdiss} \citation{samoa-phd} \citation{quodlibet-cade} \citation{wirthcardinal} \citation{wirthcardinal} \citation{SR--2011--01} \citation{kuehlerdiss} \citation{bm} \citation{kuehlerdiss} \citation{wirth-pascal} \citation{kuehlerdiss} \citation{samoa-phd} \citation{samoa-phd} \citation{jancl} \citation{samoa-phd} \citation{samoacalculemus} \citation{samoacalculemus} \citation{samoa-phd} \citation{wirth-manifesto-ljigpl} \@writefile{toc}{\contentsline {section}{\numberline {8}\MakeTextUppercase {Lessons Learned}}{88}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {8}Lessons Learned}{88}} \newlabel{section Lessons Learned}{{8}{88}} \citation{boyer-moore-2012} \citation{writing-mathematics} \citation{Boy71} \citation{boyer-moore-fast-string-searching} \citation{boyer-moore-1977} \citation{boyer-moore-proof-checking-RSA} \citation{boyer-moore-turing-completeness-lisp} \citation{boyer-moore-halting-problem} \citation{boyer-moore-1985} \citation{BM90} \citation{boyer-moore-shostak} \citation{boyer-yu-1992} \citation{moore-1979} \citation{herbrand-handbook} \citation{wirth-heijenoort} \@writefile{toc}{\contentsline {section}{\numberline {9}\MakeTextUppercase {Conclusion}}{89}} \@writefile{ptc1}{\contentsline {Psection}{\numberline {9}Conclusion}{89}} \newlabel{section Conclusion}{{9}{89}} \bibdata{herbrandbib} \bibcite{seventhPOPLeighty}{\citeauthoryear {Abrahams \bgroup \em et al.\egroup }{1980}} \bibcite{plato-induction}{\citeauthoryear {Acerbi{\acerbiindex }}{2000}} \bibcite{ackermann-1928a}{\citeauthoryear {Ackermann\ackermannindex }{1928}} \bibcite{ackermann-consistency-of-arithmetic}{\citeauthoryear {Ackermann\ackermannindex }{1940}} \bibcite{kaci-nivat}{\citeauthoryear {A{\"\i }t-Kaci and Nivat}{1989}} \bibcite{aamp7g-2005}{\citeauthoryear {Anon}{2005}} \bibcite{fourthIJCAReight}{\citeauthoryear {Armando \bgroup \em et al.\egroup }{2008}} \bibcite{aubin-1976}{\citeauthoryear {Aubin{\index {Aubin, Raymond}}}{1976}} \citation{aubin-1979} \bibcite{aubin-1979}{\citeauthoryear {Aubin{\index {Aubin, Raymond}}}{1979}} \citation{aubin-1976} \bibcite{inkafuenf}{\citeauthoryear {Autexier{\index {Autexier, Serge (*1971)}} \bgroup \em et al.\egroup }{1999}} \citation{sixteenthCADEninetynine} \bibcite{sergetableau}{\citeauthoryear {Autexier{\index {Autexier, Serge (*1971)}}}{2005}} \citation{fourteenthTABLEAUfive} \bibcite{quodlibet-cade}{\citeauthoryear {Avenhaus \bgroup \em et al.\egroup }{2003}} \citation{nineteenthCADEthree} \bibcite{nineteenthCADEthree}{\citeauthoryear {Baader}{2003}} \bibcite{baazleitschcolllog}{\citeauthoryear {Baaz and Leitsch}{1995}} \bibcite{Hotz-Festschrift}{\citeauthoryear {Bachmair \bgroup \em et al.\egroup }{1992}} \bibcite{bachmair}{\citeauthoryear {Bachmair}{1988}} \citation{lics3} \bibcite{ijcai13}{\citeauthoryear {Bajscy}{1993}} \bibcite{lambda-calculus-1st}{\citeauthoryear {Barendregt}{1981}} \citation{lambda-calculus-final} \bibcite{lambda-calculus-final}{\citeauthoryear {Barendregt}{2012}} \citation{lambda-calculus-1st} \bibcite{fermatslife-english-2}{\citeauthoryear {Barner{\index {Barner, Klaus}}}{2001a}} \citation{fermatslife} \bibcite{fermatslife}{\citeauthoryear {Barner{\index {Barner, Klaus}}}{2001b}} \citation{fermat-birth-date} \citation{fermatslife-english-1} \citation{fermatslife-english-1} \citation{fermatslife-english-2} \bibcite{fermatslife-english-1}{\citeauthoryear {Barner{\index {Barner, Klaus}}}{2001c}} \citation{fermatslife} \citation{fermat-birth-date} \bibcite{fermat-birth-date}{\citeauthoryear {Barner{\index {Barner, Klaus}}}{2007}} \citation{fermatslife-english-1} \bibcite{rippling-calculus}{\citeauthoryear {Basin and Walsh}{1996}} \bibcite{becker-griechische}{\citeauthoryear {Becker}{1965}} \bibcite{fourteenthTABLEAUfive}{\citeauthoryear {Beckert}{2005}} \bibcite{waterfall}{\citeauthoryear {Bell and Thayer}{1976}} \citation{secondICSEseventysix} \bibcite{C26}{\citeauthoryear {Benz{\discretionary {-}{}{}}m{\unprotectedue }ller{\index {Benzmueller, Christoph (*1968)@{Benzm\"uller, Christoph\ (*1968)}}} \bgroup \em et al.\egroup }{2008}} \citation{fourthIJCAReight} \bibcite{logiktexte}{\citeauthoryear {Berka and Kreiser}{1973}} \bibcite{bevers&lewi}{\citeauthoryear {Bevers and Lewi}{1990}} \citation{secondCTRSninety} \bibcite{cli-1989-1}{\citeauthoryear {Bevier \bgroup \em et al.\egroup }{1989}} \bibcite{bevier-1989}{\citeauthoryear {Bevier}{1989}} \bibcite{fifthCADEeighty}{\citeauthoryear {Bibel and Kowalski{\index {Kowalski, Robert A. (*1941)}}}{1980}} \bibcite{inka}{\citeauthoryear {Biundo \bgroup \em et al.\egroup }{1986}} \citation{eighthCADEeightysix} \bibcite{after-25-years}{\citeauthoryear {Bledsoe{\bledsoeindex } and Loveland}{1984}} \bibcite{BBH72-short}{\citeauthoryear {Bledsoe{\bledsoeindex } \bgroup \em et al.\egroup }{1971}} \citation{ijcai2} \citation{BBH72} \bibcite{BBH72}{\citeauthoryear {Bledsoe{\bledsoeindex } \bgroup \em et al.\egroup }{1972}} \citation{BBH72-short} \bibcite{Ble71}{\citeauthoryear {Bledsoe{\bledsoeindex }}{1971}} \bibcite{twentyfirstCAVnine}{\citeauthoryear {Bouajjani and Maler}{2009}} \bibcite{spike}{\citeauthoryear {Bouhoula and Rusinowitch}{1995}} \bibcite{bourbaki-set-theory-results-1st-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1939}} \citation{churchbourbaki} \citation{bourbaki-set-theory-results-2nd-edn} \bibcite{bourbaki-set-theory-results-2nd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1951}} \citation{bourbaki-set-theory-results-1st-edn} \citation{bourbaki-set-theory-results-3rd-edn} \bibcite{bourbaki-set-theory-chapter-1-2-1st-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1954}} \citation{bourbaki-set-theory-chapter-1-2-2nd-edn} \bibcite{bourbaki-set-theory-chapter-3-1st-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1956}} \citation{bourbaki-set-theory-chapter-3-2nd-edn} \bibcite{bourbaki-set-theory-chapter-4-1st-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1958a}} \citation{bourbaki-set-theory-chapter-4-2nd-edn} \bibcite{bourbaki-set-theory-results-3rd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1958b}} \citation{bourbaki-set-theory-results-2nd-edn} \citation{bourbaki-set-theory-results-4th-edn} \bibcite{bourbaki-set-theory-chapter-1-2-2nd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1960}} \citation{bourbaki-set-theory-chapter-1-2-1st-edn} \citation{bourbaki-set-theory-chapter-1-2-3rd-edn} \bibcite{bourbaki-set-theory-results-4th-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1964}} \citation{bourbaki-set-theory-results-3rd-edn} \citation{bourbaki-set-theory-results-5th-edn} \bibcite{bourbaki-set-theory-chapter-4-2nd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1966a}} \citation{bourbaki-set-theory-chapter-4-1st-edn} \citation{bourbaki-english} \bibcite{bourbaki-set-theory-chapter-1-2-3rd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1966b}} \citation{bourbaki-set-theory-chapter-1-2-2nd-edn} \citation{bourbaki-english} \bibcite{bourbaki-set-theory-chapter-3-2nd-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1967}} \citation{bourbaki-set-theory-chapter-3-1st-edn} \citation{bourbaki-english} \bibcite{bourbaki-english}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1968a}} \citation{bourbaki-set-theory-chapter-1-2-3rd-edn} \citation{bourbaki-set-theory-chapter-1-2-3rd-edn} \citation{bourbaki-set-theory-chapter-3-2nd-edn} \citation{bourbaki-set-theory-chapter-4-2nd-edn} \citation{bourbaki-set-theory-results-5th-edn} \bibcite{bourbaki-set-theory-results-5th-edn}{\citeauthoryear {Bourbaki{\index {Bourbaki, Nicolas (pseudonym)}}}{1968b}} \citation{bourbaki-set-theory-results-4th-edn} \citation{bourbaki-english} \bibcite{boyer-moore-1971}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1971}} \citation{boyer-moore-1972} \bibcite{boyer-moore-1972}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1972}} \citation{machine-intelligence-7} \bibcite{boyer-moore-1973}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1973}} \citation{ijcai3} \citation{boyer-moore-1975} \bibcite{boyer-moore-1975}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1975}} \citation{boyer-moore-1973} \bibcite{boyer-moore-fast-string-searching}{\citeauthoryear {Boyer{\boyerindex \index {Boyer--Moore fast string searching algorithm}} and Moore{\mooreindex }}{1977a}} \bibcite{boyer-moore-1977}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1977b}} \citation{ijcai5} \bibcite{bm}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1979}} \bibcite{boyer-moore-1981-editors}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1981a}} \bibcite{boyer-moore-1981-authors}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1981b}} \citation{boyer-moore-1981-editors} \bibcite{boyer-moore-turing-completeness-lisp}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1984a}} \citation{after-25-years} \bibcite{boyer-moore-halting-problem}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1984b}} \bibcite{boyer-moore-proof-checking-RSA}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1984c}} \bibcite{boyer-moore-1985}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1985}} \bibcite{bmeval-1987}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1987}} \citation{bmeval-1988} \citation{bmeval-1988} \citation{bmeval-1989} \bibcite{bmeval-1988}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1988a}} \citation{bmeval-1987} \citation{bmeval-1987} \citation{bmeval-1989} \bibcite{boyermoore}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1988b}} \citation{boyermooresecondedition} \bibcite{boyer-moore-1988}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1988c}} \citation{machine-intelligence-11} \bibcite{bmeval-1989}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1989}} \citation{broy-1989} \citation{bmeval-1987} \citation{bmeval-1987} \citation{bmeval-1988} \bibcite{BM90}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1990}} \citation{tenthCADEninety} \bibcite{boyermooresecondedition}{\citeauthoryear {Boyer{\boyerindex } and Moore{\mooreindex }}{1998}} \citation{boyermoore} \bibcite{boyer-yu-1992}{\citeauthoryear {Boyer{\boyerindex } and Yu}{1992}} \citation{eleventhCADEninetytwo} \bibcite{c-string-lib-1996}{\citeauthoryear {Boyer{\boyerindex } and Yu}{1996}} \bibcite{boyer-moore-davies-1973}{\citeauthoryear {Boyer{\boyerindex } \bgroup \em et al.\egroup }{1973}} \bibcite{boyer-moore-shostak}{\citeauthoryear {Boyer{\boyerindex } \bgroup \em et al.\egroup }{1976}} \citation{thirdPOPLseventysix} \bibcite{Boy71}{\citeauthoryear {Boyer{\boyerindex }}{1971}} \bibcite{boyer-2012}{\citeauthoryear {Boyer{\boyerindex }}{2012}} \bibcite{brock-hunt-1999}{\citeauthoryear {Brock and Hunt{\index {Hunt, Warren A.}}}{1999}} \citation{industrial-strength-1999} \bibcite{DBLP:conf/lics/BrotherstonS07}{\citeauthoryear {Brotherston and Simpson}{2007}} \citation{lics22} \citation{brotherston-cut-elimination} \bibcite{brotherston-cut-elimination}{\citeauthoryear {Brotherston and Simpson}{2011}} \citation{DBLP:conf/tableaux/Brotherston05} \citation{DBLP:conf/lics/BrotherstonS07} \bibcite{DBLP:conf/tableaux/Brotherston05}{\citeauthoryear {Brotherston}{2005}} \citation{fourteenthTABLEAUfive} \citation{brotherston-cut-elimination} \bibcite{satallax}{\citeauthoryear {Brown}{2012}} \citation{sixthIJCARtwelve} \bibcite{broy-1989}{\citeauthoryear {Broy}{1989}} \bibcite{waldmeister}{\citeauthoryear {Buch and Hillenbrand{\index {Hillenbrand, Thomas}}}{1996}} \bibcite{bundy-recursion-analysis}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}} \bgroup \em et al.\egroup }{1989}} \citation{ijcai11} \bibcite{oysterclam}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}} \bgroup \em et al.\egroup }{1990}} \citation{tenthCADEninety} \bibcite{rippling}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}} \bgroup \em et al.\egroup }{1991}} \bibcite{rippling-book}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}} \bgroup \em et al.\egroup }{2005}} \bibcite{bundy-inductive-proof-planning}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}}}{1988}} \citation{ninthCADEeightyeight} \bibcite{science-of-reasoning}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}}}{1989}} \citation{honor-robinson} \bibcite{twelvethCADEninetyfour}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}}}{1994}} \bibcite{bundy-survey}{\citeauthoryear {Bundy{\index {Bundy, Alan (*1947)}}}{1999}} \citation{HandbookAR} \bibcite{pop2}{\citeauthoryear {Burstall{\index {Burstall, Rod M. (*1934)}} \bgroup \em et al.\egroup }{1971}} \bibcite{burstall-1969}{\citeauthoryear {Burstall{\index {Burstall, Rod M. (*1934)}}}{1969}} \bibcite{maurolycus}{\citeauthoryear {Bussey}{1917}} \bibcite{From-Fermat-to-Gauss}{\citeauthoryear {Bussotti}{2006}} \bibcite{cajori-1918}{\citeauthoryear {Cajori}{1918}} \bibcite{churchbourbaki}{\citeauthoryear {Church}{1946}} \citation{bourbaki-set-theory-results-1st-edn} \bibcite{Prolog}{\citeauthoryear {Clocksin and Mellish}{2003}} \bibcite{cohn-1965}{\citeauthoryear {Cohn}{1965}} \citation{cohn-1981} \bibcite{cohn-1981}{\citeauthoryear {Cohn}{1981}} \citation{cohn-1965} \bibcite{eighthRTAninetyseven}{\citeauthoryear {Comon}{1997}} \bibcite{comonAR}{\citeauthoryear {Comon}{2001}} \citation{HandbookAR} \bibcite{nuprl-book}{\citeauthoryear {Constable \bgroup \em et al.\egroup }{1985}} \bibcite{ijcai2}{\citeauthoryear {Cooper}{1971}} \bibcite{dac/2001}{\citeauthoryear {DAC}{2001}} \bibcite{darlington-1968}{\citeauthoryear {Darlington}{1968}} \citation{machine-intelligence-3} \bibcite{davis-2009}{\citeauthoryear {Davis}{2009}} \bibcite{dedekind-1888}{\citeauthoryear {Dedekind{\dedekindindex }}{1888}} \citation{dedekind-1930-32} \citation{dedekind-1969} \bibcite{dedekind-1930-32}{\citeauthoryear {Dedekind{\dedekindindex }}{1930--32}} \bibcite{dedekind-1969}{\citeauthoryear {Dedekind{\dedekindindex }}{1969}} \bibcite{proofplanningsystems}{\citeauthoryear {Dennis \bgroup \em et al.\egroup }{2005}} \bibcite{term-rewriting-one}{\citeauthoryear {Dershowitz and Jouannaud}{1990}} \citation{handbook-tcs} \bibcite{fourthCTRSninetyfour}{\citeauthoryear {Dershowitz and Lindenstrauss}{1995}} \bibcite{thirdRTAeightynine}{\citeauthoryear {Dershowitz}{1989}} \bibcite{dodi-diss}{\citeauthoryear {Dietrich}{2011}} \bibcite{elements}{\citeauthoryear {Euclid{\euclidindex }}{ca.\,300\,{\sc b.c.}}} \bibcite{fermat-oeuvres}{\citeauthoryear {Fermat}{1891\unhbox \voidb@x \hbox {}{ff.}}} \bibcite{Fitting90}{\citeauthoryear {Fitting}{1990}} \citation{fitting} \bibcite{fitting}{\citeauthoryear {Fitting}{1996}} \citation{Fitting90} \bibcite{focs21}{\citeauthoryear {FOCS}{1980}} \bibcite{Greeks-induction}{\citeauthoryear {Fowler}{1994}} \bibcite{freudenthal}{\citeauthoryear {Freudenthal}{1953}} \bibcite{inductionlesshistb}{\citeauthoryear {Fribourg}{1986}} \citation{thirteenthICALPeightysix} \bibcite{fries-vollstaendige-induction}{\citeauthoryear {Fries{\index {Fries, Jakob Friedrich (1773--1843)}}}{1822}} \bibcite{hippa}{\citeauthoryear {Fritz}{1945}} \citation{becker-griechische} \bibcite{future-generation}{\citeauthoryear {Fuchi and Kott}{1988}} \bibcite{handbook-of-the-history-of-logic}{\citeauthoryear {Gabbay{\index {Gabbay, Dov (*1945)}} and Woods}{2004\unhbox \voidb@x \hbox {}{ff.}}} \bibcite{handbooklogicailpvol2}{\citeauthoryear {Gabbay{\index {Gabbay, Dov (*1945)}} \bgroup \em et al.\egroup }{1994}} \bibcite{GaSt}{\citeauthoryear {Ganzinger and Stuber}{1992}} \citation{Hotz-Festschrift} \citation{thirdCTRSninetytwo} \bibcite{seventhRTAninetysix}{\citeauthoryear {Ganzinger}{1996}} \bibcite{sixteenthCADEninetynine}{\citeauthoryear {Ganzinger}{1999}} \bibcite{gentzen}{\citeauthoryear {Gentzen}{1935}} \citation{logiktexte} \citation{gentzen-collected} \bibcite{gentzen-collected}{\citeauthoryear {Gentzen}{1969}} \bibcite{geseraxiomofchoice}{\citeauthoryear {Geser}{1995}} \citation{Kolloquium-Programmiersprachen-und-Grundlagen-der-Programmierung} \bibcite{geser-improved-general-path-order}{\citeauthoryear {Geser}{1996}} \bibcite{writing-mathematics}{\citeauthoryear {Gillman}{1987}} \bibcite{inductionlesshistc}{\citeauthoryear {G{\"o}bel}{1985}} \citation{gwai9} \bibcite{goedel}{\citeauthoryear {G{\unprotectedoe de{\index {Goedel, Kurt@G\"odel, Kurt (1906--1978)}}l}}{1931}} \citation{goedelcollected} \citation{heijenoort-source-book} \citation{goedel-meltzer} \bibcite{goedel-meltzer}{\citeauthoryear {G{\unprotectedoe de{\index {Goedel, Kurt@G\"odel, Kurt (1906--1978)}}l}}{1962}} \citation{goedel} \bibcite{goedelcollected}{\citeauthoryear {G{\unprotectedoe de{\index {Goedel, Kurt@G\"odel, Kurt (1906--1978)}}l}}{1986ff.}} \bibcite{gogueninductionlessinduction}{\citeauthoryear {Goguen}{1980}} \citation{fifthCADEeighty} \bibcite{catherine-goldstein-fermat-priceton-companion-math-2008}{\citeauthoryear {Goldstein{\index {Goldstein, Catherine (*1958)}}}{2008}} \citation{priceton-companion-math-2008} \bibcite{fromLCFtoHOL}{\citeauthoryear {Gordon{\index {Gordon, Mike J. C. (*1948)}}}{2000}} \citation{honorrobinmilner} \bibcite{firstIJCARone}{\citeauthoryear {Gore \bgroup \em et al.\egroup }{2001}} \bibcite{priceton-companion-math-2008}{\citeauthoryear {Gowers \bgroup \em et al.\egroup }{2008}} \bibcite{thirdPOPLseventysix}{\citeauthoryear {Graham \bgroup \em et al.\egroup }{1976}} \bibcite{unicom}{\citeauthoryear {Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (*1959)}}ch and Lindner}{1991}} \bibcite{gwrta}{\citeauthoryear {Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (*1959)}}ch and Wirth{\index {Wirth, Claus-Peter (*1963)}}}{1996}} \citation{seventhRTAninetysix} \bibcite{sixthIJCARtwelve}{\citeauthoryear {Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (*1959)}}ch \bgroup \em et al.\egroup }{2012}} \bibcite{machine-intelligence-11}{\citeauthoryear {Hayes \bgroup \em et al.\egroup }{1988}} \bibcite{heijenoort-source-book}{\citeauthoryear {Heijenoort{\heijenoortindex }}{1971}} \bibcite{Coq1}{\citeauthoryear {Herbelin}{2009}} \bibcite{grundlagen-first-edition-volume-one}{\citeauthoryear {Hilbe{\index {Hilbert, David (1862--1943)}}rt and Bernays\bernaysindex }{1934}} \citation{grundlagen-second-edition-volume-one} \bibcite{grundlagen-first-edition-volume-two}{\citeauthoryear {Hilbe{\index {Hilbert, David (1862--1943)}}rt and Bernays\bernaysindex }{1939}} \citation{grundlagen-second-edition-volume-two} \bibcite{grundlagen-second-edition-volume-one}{\citeauthoryear {Hilbe{\index {Hilbert, David (1862--1943)}}rt and Bernays\bernaysindex }{1968}} \citation{grundlagen-first-edition-volume-one} \bibcite{grundlagen-second-edition-volume-two}{\citeauthoryear {Hilbe{\index {Hilbert, David (1862--1943)}}rt and Bernays\bernaysindex }{1970}} \citation{grundlagen-first-edition-volume-two} \bibcite{grundlagen-german-english-edition-volume-one-one}{\citeauthoryear {Hilbe{\index {Hilbert, David (1862--1943)}}rt and Bernays\bernaysindex }{2013}} \citation{grundlagen-second-edition-volume-one} \citation{grundlagen-first-edition-volume-one} \bibcite{HL02}{\citeauthoryear {Hillenbrand{\index {Hillenbrand, Thomas}} and L{\unprotectedoe }chner{\index {Loechner, Bernd (*1967)@{L\"ochner, Bernd (*1967)}}}}{2002}} \citation{eightteenthCADEtwo} \bibcite{industrial-strength-1999}{\citeauthoryear {Hinchey and Bowen}{1999}} \bibcite{5-int-congress-mathematicians-1912}{\citeauthoryear {Hobson and Love}{1913}} \bibcite{weakaxiomofchoice}{\citeauthoryear {Howard and Rubin}{1998}} \bibcite{haskell}{\citeauthoryear {Hudlak \bgroup \em et al.\egroup }{1999}} \bibcite{huethullotinductionlessinduction}{\citeauthoryear {Huet and Hullot}{1980}} \citation{focs21} \bibcite{huet}{\citeauthoryear {Huet}{1980}} \bibcite{hunt-swords-2009}{\citeauthoryear {Hunt{\index {Hunt, Warren A.}} and Swords}{2009}} \citation{twentyfirstCAVnine} \bibcite{hunt-1985}{\citeauthoryear {Hunt{\index {Hunt, Warren A.}}}{1985}} \citation{hunt-1994} \bibcite{hunt-1989}{\citeauthoryear {Hunt{\index {Hunt, Warren A.}}}{1989}} \bibcite{hunt-1994}{\citeauthoryear {Hunt{\index {Hunt, Warren A.}}}{1994}} \citation{hunt-1985} \bibcite{inductioncontest}{\citeauthoryear {Hutter{\index {Hutter, Dieter (*1959)}} and Bundy{\index {Bundy, Alan (*1947)}}}{1999}} \citation{sixteenthCADEninetynine} \bibcite{inkanext}{\citeauthoryear {Hutter{\index {Hutter, Dieter (*1959)}} and Sengler}{1996}} \citation{thirteenthCADEninetysix} \bibcite{siekmann-60}{\citeauthoryear {Hutter{\index {Hutter, Dieter (*1959)}} and Stephan}{2005}} \bibcite{hutter-rippling}{\citeauthoryear {Hutter{\index {Hutter, Dieter (*1959)}}}{1990}} \citation{tenthCADEninety} \bibcite{failure-guide-induction}{\citeauthoryear {Ireland and Bundy{\index {Bundy, Alan (*1947)}}}{1994}} \bibcite{automatic-learning-proof-planning}{\citeauthoryear {Jamnik \bgroup \em et al.\egroup }{2003}} \bibcite{inductionlesshista}{\citeauthoryear {Jouannaud and Kounalis}{1986}} \citation{lics1} \bibcite{firstCTRSeightyseven}{\citeauthoryear {Kaplan and Jouannaud}{1988}} \bibcite{secondCTRSninety}{\citeauthoryear {Kaplan and Okada}{1991}} \bibcite{kapur2}{\citeauthoryear {Kapur and Musser}{1986}} \citation{lics1} \bibcite{kapur1}{\citeauthoryear {Kapur and Musser}{1987}} \bibcite{mutualexplicitinduction}{\citeauthoryear {Kapur and Subramaniam}{1996}} \citation{fifthAMASTninetysix} \bibcite{rrl}{\citeauthoryear {Kapur and Zhang}{1989}} \citation{thirdRTAeightynine} \citation{Kapur95} \bibcite{Kapur95}{\citeauthoryear {Kapur and Zhang}{1995}} \bibcite{eleventhCADEninetytwo}{\citeauthoryear {Kapur}{1992}} \bibcite{katz-history}{\citeauthoryear {Katz}{1998}} \bibcite{ACLTWO-CASESTUDIES}{\citeauthoryear {Kaufmann{\index {Kaufmann, Matt (*1952)}} \bgroup \em et al.\egroup }{2000a}} \bibcite{ACLTWO}{\citeauthoryear {Kaufmann{\index {Kaufmann, Matt (*1952)}} \bgroup \em et al.\egroup }{2000b}} \bibcite{KB70}{\citeauthoryear {Knuth and Bendix}{1970}} \citation{leech-1970} \bibcite{eighthECAIeightyeight}{\citeauthoryear {Kodratoff}{1988}} \bibcite{thirteenthICALPeightysix}{\citeauthoryear {Kott}{1986}} \bibcite{Kow74}{\citeauthoryear {Kowalski{\index {Kowalski, Robert A. (*1941)}}}{1974}} \citation{IFIP-1974} \bibcite{kowalski-1988}{\citeauthoryear {Kowalski{\index {Kowalski, Robert A. (*1941)}}}{1988}} \bibcite{induction-no-cut}{\citeauthoryear {Kreisel}{1965}} \citation{saaty} \bibcite{inductionlesshistd}{\citeauthoryear {K{\"u}chlin}{1989}} \citation{kaci-nivat} \bibcite{kwspec}{\citeauthoryear {K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}} and Wirth{\index {Wirth, Claus-Peter (*1963)}}}{1996}} \citation{kwspec2} \bibcite{kwspec2}{\citeauthoryear {K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}} and Wirth{\index {Wirth, Claus-Peter (*1963)}}}{1997}} \citation{eighthRTAninetyseven} \citation{kwspec} \bibcite{kuehler-master}{\citeauthoryear {K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}}{1991}} \bibcite{kuehlerdiss}{\citeauthoryear {K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}}{2000}} \bibcite{lambert-1764}{\citeauthoryear {Lambert}{1764}} \bibcite{inductionlessinduction1}{\citeauthoryear {Lankford}{1980}} \bibcite{inductionlessinduction2}{\citeauthoryear {Lankford}{1981}} \bibcite{honor-robinson}{\citeauthoryear {Lassez and Plotkin}{1991}} \bibcite{leech-1970}{\citeauthoryear {Leech}{1970}} \bibcite{handbook-tcs}{\citeauthoryear {Leeuwen}{1990}} \bibcite{lics1}{\citeauthoryear {LICS}{1986}} \bibcite{lics3}{\citeauthoryear {LICS}{1988}} \bibcite{lics22}{\citeauthoryear {LICS}{2007}} \bibcite{loechner-lpo}{\citeauthoryear {L{\unprotectedoe }chner{\index {Loechner, Bernd (*1967)@{L\"ochner, Bernd (*1967)}}}}{2006}} \bibcite{ninthCADEeightyeight}{\citeauthoryear {Lusk and Overbeek}{1988}} \bibcite{fermat-career}{\citeauthoryear {Mahoney}{1994}} \bibcite{smith-pieri}{\citeauthoryear {Marchisotto and Smit{\index {Smith, James T.}}h}{2007}} \bibcite{Kolloquium-Programmiersprachen-und-Grundlagen-der-Programmierung}{\citeauthoryear {Margaria}{1995}} \bibcite{LISP}{\citeauthoryear {McCarthy \bgroup \em et al.\egroup }{1965}} \bibcite{thirteenthCADEninetysix}{\citeauthoryear {McRobbie and Slaney}{1996}} \bibcite{proof_planning_with_multiple_strategies}{\citeauthoryear {Melis \bgroup \em et al.\egroup }{2008}} \bibcite{machine-intelligence-7}{\citeauthoryear {Meltzer{\index {Meltzer, Bernard (1916?--2008)}} and Michie{\index {Michie, Donald (1923--2007)}}}{1972}} \bibcite{meltzer-1975}{\citeauthoryear {Meltzer{\index {Meltzer, Bernard (1916?--2008)}}}{1975}} \bibcite{machine-intelligence-3}{\citeauthoryear {Michie{\index {Michie, Donald (1923--2007)}}}{1968}} \bibcite{milner-1972}{\citeauthoryear {Milner}{1972}} \bibcite{moore-lynch-kaufmann-1998}{\citeauthoryear {Moore{\mooreindex } \bgroup \em et al.\egroup }{1998}} \bibcite{moore-1973}{\citeauthoryear {Moore{\mooreindex }}{1973}} \bibcite{moore-1975}{\citeauthoryear {Moore{\mooreindex }}{1975a}} \citation{moore-1975-short} \bibcite{moore-1975-short}{\citeauthoryear {Moore{\mooreindex }}{1975b}} \citation{moore-1975} \bibcite{moore-1979}{\citeauthoryear {Moore{\mooreindex }}{1979}} \bibcite{moore-1981}{\citeauthoryear {Moore{\mooreindex }}{1981}} \bibcite{moore-1989-2}{\citeauthoryear {Moore{\mooreindex }}{1989a}} \bibcite{moore-1989-1}{\citeauthoryear {Moore{\mooreindex }}{1989b}} \bibcite{chaff}{\citeauthoryear {Moskewicz \bgroup \em et al.\egroup }{2001}} \citation{dac/2001} \bibcite{musserinductionlessinduction}{\citeauthoryear {Musser}{1980}} \citation{seventhPOPLeighty} \bibcite{ijcai3}{\citeauthoryear {Nilsson}{1973}} \bibcite{padawitzjsc}{\citeauthoryear {Padawitz}{1996}} \bibcite{padoa-1913}{\citeauthoryear {Padoa{\index {Padoa, Alessandro (1868--1937)}}}{1913}} \citation{5-int-congress-mathematicians-1912} \bibcite{pascal}{\citeauthoryear {Pascal}{1954}} \bibcite{Pau96}{\citeauthoryear {Paulson}{1996}} \bibcite{peanonovamethodo}{\citeauthoryear {Peano{\peanoindex }}{1889}} \bibcite{peter-1951}{\citeauthoryear {P{\'e}ter{\index {P\'eter, R\'osza (1905--1977)}}}{1951}} \bibcite{pieri}{\citeauthoryear {Pieri{\pieriindex }}{1908}} \citation{smith-pieri} \bibcite{honorrobinmilner}{\citeauthoryear {Plotkin \bgroup \em et al.\egroup }{2000}} \bibcite{presburger}{\citeauthoryear {Presburger{\presburgerindex }}{1930}} \citation{presburger-remarks-translation} \bibcite{protzenlazy}{\citeauthoryear {Protzen{\index {Protzen, Martin (*1962)}}}{1994}} \citation{twelvethCADEninetyfour} \bibcite{protzendiss}{\citeauthoryear {Protzen{\index {Protzen, Martin (*1962)}}}{1995}} \bibcite{protzenpatching}{\citeauthoryear {Protzen{\index {Protzen, Martin (*1962)}}}{1996}} \citation{thirteenthCADEninetysix} \bibcite{Ravinovitch-Gershon}{\citeauthoryear {Rabinovitch}{1970}} \bibcite{ijcai5}{\citeauthoryear {Reddy}{1977}} \bibcite{reddy}{\citeauthoryear {Reddy}{1990}} \citation{tenthCADEninety} \bibcite{vampire01}{\citeauthoryear {Riazanov and Voronkov}{2001}} \citation{firstIJCARone} \bibcite{HandbookAR}{\citeauthoryear {Robinson{\index {Robinson, J. Alan (*1930?)}} and Voronkow}{2001}} \bibcite{IFIP-1974}{\citeauthoryear {Rosenfeld}{1974}} \bibcite{axiomofchoice}{\citeauthoryear {Rubin and Rubin}{1985}} \bibcite{thirdCTRSninetytwo}{\citeauthoryear {Rusinowitch and Remy}{1993}} \bibcite{russinoff-1998}{\citeauthoryear {Russinoff}{1998}} \bibcite{saaty}{\citeauthoryear {Saaty}{1965}} \bibcite{samoacalculemus}{\citeauthoryear {Schmidt-Samoa{\index {Schmidt-Samoa, Tobias (*1973)}}}{2006a}} \bibcite{samoa-phd}{\citeauthoryear {Schmidt-Samoa{\index {Schmidt-Samoa, Tobias (*1973)}}}{2006b}} \bibcite{jancl}{\citeauthoryear {Schmidt-Samoa{\index {Schmidt-Samoa, Tobias (*1973)}}}{2006c}} \bibcite{schoenfield}{\citeauthoryear {Schoenfield}{1967}} \bibcite{scott-LCF}{\citeauthoryear {Scott{\index {Scott, Dana S. (*1932)}}}{1993}} \bibcite{shankar-1986}{\citeauthoryear {Shankar{\index {Shankar, Natarajan}}}{1986}} \citation{shankar-1994} \bibcite{church-rosser-bm}{\citeauthoryear {Shankar{\index {Shankar, Natarajan}}}{1988}} \citation{shankar-1994} \bibcite{shankar-1994}{\citeauthoryear {Shankar{\index {Shankar, Natarajan}}}{1994}} \citation{shankar-1986} \bibcite{eighthCADEeightysix}{\citeauthoryear {Siek{\discretionary {-}{}{}}mann{\siekmannindex }}{1986}} \bibcite{ijcai11}{\citeauthoryear {Sridharan}{1989}} \bibcite{presburger-remarks-translation}{\citeauthoryear {Stansifer}{1984}} \bibcite{commonlisp}{\citeauthoryear {Steele}{1990}} \bibcite{SR--88--12}{\citeauthoryear {Steinbach}{1988}} \bibcite{simplificationorderings}{\citeauthoryear {Steinbach}{1995}} \bibcite{stevens-rational-reconstruction}{\citeauthoryear {Stevens}{1988}} \citation{eighthECAIeightyeight} \bibcite{tenthCADEninety}{\citeauthoryear {Stickel}{1990}} \bibcite{gwai9}{\citeauthoryear {Stoyan}{1985}} \bibcite{toyama}{\citeauthoryear {Toyama}{1988}} \citation{future-generation} \citation{toyamadiss} \bibcite{toyamadiss}{\citeauthoryear {Toyama}{1990}} \bibcite{unguru-one}{\citeauthoryear {Unguru}{1991}} \bibcite{simonyi-interview}{\citeauthoryear {Verma}{2005?}} \bibcite{voicu-li-di}{\citeauthoryear {Voicu and Li}{2009}} \citation{Coq1} \bibcite{thirdLPARninetytwo}{\citeauthoryear {Voronkov}{1992}} \bibcite{eightteenthCADEtwo}{\citeauthoryear {Voronkov}{2002}} \bibcite{walthertermination}{\citeauthoryear {Walther{\index {Walther, Christoph (*1950)}}}{1988}} \citation{ninthCADEeightyeight} \bibcite{waltherLPAR92}{\citeauthoryear {Walther{\index {Walther, Christoph (*1950)}}}{1992}} \citation{thirdLPARninetytwo} \bibcite{waltherIJCAI93}{\citeauthoryear {Walther{\index {Walther, Christoph (*1950)}}}{1993}} \citation{ijcai13} \bibcite{waltherhandbook}{\citeauthoryear {Walther{\index {Walther, Christoph (*1950)}}}{1994a}} \citation{handbooklogicailpvol2} \bibcite{walthertermination2}{\citeauthoryear {Walther{\index {Walther, Christoph (*1950)}}}{1994b}} \bibcite{fifthAMASTninetysix}{\citeauthoryear {Wirsing and Nivat}{1996}} \bibcite{wirthbecker}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} and Becker}{1995}} \citation{fourthCTRSninetyfour} \bibcite{wgjsc}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} and Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (*1959)}}ch}{1994a}} \bibcite{wgcade}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} and Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (*1959)}}ch}{1994b}} \citation{twelvethCADEninetyfour} \bibcite{SR--95--15}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} and K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}}{1995}} \bibcite{wgkp}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \em et al.\egroup }{1993}} \citation{wgjsc} \citation{wgcade} \bibcite{herbrand-handbook}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \em et al.\egroup }{2009}} \citation{handbook-of-the-history-of-logic} \bibcite{wirth-pascal}{\citeauthoryear {Wirth}{1971}} \bibcite{wirth-master}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{1991}} \bibcite{wirthdiss}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{1997}} \bibcite{wirthcardinal}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2004}} \bibcite{zombie}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2005a}} \citation{siekmann-60} \bibcite{wirthconfluence}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2005b}} \bibcite{nonpermut}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2006}} \citation{wirth-jsc-non-permut} \bibcite{wirth-jsc}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2009}} \bibcite{swp200601}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2010a}} \bibcite{fermatsproof}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2010b}} \bibcite{wirth-heijenoort}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2012a}} \bibcite{wirth-jsc-non-permut}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2012b}} \citation{nonpermut} \bibcite{wirth-manifesto-ljigpl}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2012c}} \bibcite{boyer-moore-2012}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2012d}} \bibcite{SR--2011--01}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}}}{2013}} \bibcite{wolff-rationalis}{\citeauthoryear {Wolff}{1728}} \bibcite{wolff-rationalis-1740}{\citeauthoryear {Wolff}{1740}} \citation{wolff-rationalis} \bibcite{secondICSEseventysix}{\citeauthoryear {Yeh and Ramamoorthy}{1976}} \bibcite{young-1989}{\citeauthoryear {Young}{1989}} \bibcite{ZKK88}{\citeauthoryear {Zhang \bgroup \em et al.\egroup }{1988}} \citation{ninthCADEeightyeight} \bibcite{presburger-life}{\citeauthoryear {Zygmunt}{1991}} \@writefile{toc}{\contentsline {chapter}{INDEX}{105}}