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{McCarthy \bgroup \&al.\egroup }{1965}} \bibcite{thirteenthCADEninetysix}{\citeauthoryear {McRobbie \bgroup \&\ \egroup Slaney}{1996}} \bibcite{proof_planning_with_multiple_strategies}{\citeauthoryear {Melis \bgroup \&al.\egroup }{2008}} \bibcite{meltzer-1975}{\citeauthoryear {Meltzer{\index {Meltzer, Bernard (1916(?)--2008)}}}{1975}} \bibcite{machine-intelligence-7}{\citeauthoryear {Meltzer{\index {Meltzer, Bernard (1916(?)--2008)}} \bgroup \&\ \egroup Michie{\index {Michie, Donald (1923--2007)}}}{1972}} \bibcite{machine-intelligence-3}{\citeauthoryear {Michie{\index {Michie, Donald (1923--2007)}}}{1968}} \bibcite{milner-1972}{\citeauthoryear {Milner}{1972}} \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{moore-lynch-kaufmann-1998}{\citeauthoryear {Moore{\mooreindex } \bgroup \&al.\egroup }{1998}} \bibcite{chaff}{\citeauthoryear {Moskewicz \bgroup \&al.\egroup }{2001}} \citation{dac/2001} \bibcite{musserinductionlessinduction}{\citeauthoryear {Musser}{1980}} \citation{seventhPOPLeighty} \bibcite{ijcai3}{\citeauthoryear {Nilsson}{1973}} \bibcite{odifreddi}{\citeauthoryear {Odifreddi}{1990}} \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{isabellesevenhundred}{\citeauthoryear {Paulson}{1990}} \citation{odifreddi} \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 \&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 \bgroup \&\ \egroup Voronkov}{2001}} \citation{firstIJCARone} \bibcite{HandbookAR}{\citeauthoryear {Robinson{\index {Robinson, J. Alan (*1930(?))}} \bgroup \&\ \egroup Voronkow}{2001}} \bibcite{IFIP-1974}{\citeauthoryear {Rosenfeld}{1974}} \bibcite{waterfallfirst}{\citeauthoryear {Royce}{1970}} \citation{ieeeweston70} \bibcite{axiomofchoice}{\citeauthoryear {Rubin{\index {Rubin, Herman (*1926)}} \bgroup \&\ \egroup Rubin{\index {Rubin, Jean E. (1926--2002)}}}{1985}} \bibcite{thirdCTRSninetytwo}{\citeauthoryear {Rusinowitch \bgroup \&\ \egroup 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{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{course-of-values-induction}{\citeauthoryear {Shepherdson}{1969}} \bibcite{Shoenfield67}{\citeauthoryear {Shoenfield{\index {Shoenfield, Joseph R. (1927--2000)}}}{1967}} \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 \bgroup \&\ \egroup 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 \bgroup \&\ \egroup Nivat}{1996}} \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{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}} \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)}}}{2015}} \bibcite{wirthbecker}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&\ \egroup Becker}{1995}} \citation{fourthCTRSninetyfour} \bibcite{wgjsc}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&\ \egroup Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (1959--2014)}}ch}{1994a}} \bibcite{wgcade}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&\ \egroup Gram{\discretionary {-}{}{}}li{\index {Gramlich, Bernhard (1959--2014)}}ch}{1994b}} \citation{twelvethCADEninetyfour} \bibcite{wgkp}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&al.\egroup }{1993}} \citation{wgjsc} \citation{wgcade} \bibcite{SR--95--15}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&\ \egroup K{\"u}hler{\index {Kuehler, Ulrich (*1964)@{K\"uhler, Ulrich (*1964)}}}}{1995}} \bibcite{herbrand-handbook}{\citeauthoryear {Wirth{\index {Wirth, Claus-Peter (*1963)}} \bgroup \&al.\egroup }{2009}} \citation{handbook-of-the-history-of-logic} \bibcite{wirth-pascal}{\citeauthoryear {Wirth}{1971}} \bibcite{wolff-rationalis}{\citeauthoryear {Wolff}{1728}} \bibcite{wolff-rationalis-1740}{\citeauthoryear {Wolff}{1740}} \citation{wolff-rationalis} \bibcite{secondICSEseventysix}{\citeauthoryear {Yeh \bgroup \&\ \egroup Ramamoorthy}{1976}} \bibcite{young-1989}{\citeauthoryear {Young}{1989}} \bibcite{ZKK88}{\citeauthoryear {Zhang \bgroup \&al.\egroup }{1988}} \citation{ninthCADEeightyeight} \bibcite{presburger-life}{\citeauthoryear {Zygmunt}{1991}} \@writefile{toc}{\contentsline {section}{Index}{108}}