This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2008.12.1)  15 MAY 2010 16:31
entering extended mode
 %&-line parsing enabled.
**main
(./main.tex
LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, arabic, basque, bulgarian, coptic, welsh, czech, slovak, german, ng
erman, danish, esperanto, spanish, catalan, galician, estonian, farsi, finnish,
 french, greek, monogreek, ancientgreek, croatian, hungarian, interlingua, ibyc
us, indonesian, icelandic, italian, latin, mongolian, dutch, norsk, polish, por
tuguese, pinyin, romanian, russian, slovenian, uppersorbian, serbian, swedish, 
turkish, ukenglish, ukrainian, loaded.
(./llncs.cls
Document Class: llncs 2000/05/16 v2.8 
LaTeX document class for Lecture Notes in Computer Science
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
(/usr/share/texmf/tex/latex/base/size10.clo
File: size10.clo 2005/09/16 v1.4f Standard LaTeX file (size option)
)
\c@part=\count79
\c@section=\count80
\c@subsection=\count81
\c@subsubsection=\count82
\c@paragraph=\count83
\c@subparagraph=\count84
\c@figure=\count85
\c@table=\count86
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
)
(/usr/share/texmf/tex/latex/tools/multicol.sty
Package: multicol 2006/05/18 v1.6g multicolumn formatting (FMi)
\c@tracingmulticols=\count87
\mult@box=\box26
\multicol@leftmargin=\dimen103
\c@unbalance=\count88
\c@collectmore=\count89
\doublecol@number=\count90
\multicoltolerance=\count91
\multicolpretolerance=\count92
\full@width=\dimen104
\page@free=\dimen105
\premulticols=\dimen106
\postmulticols=\dimen107
\multicolsep=\skip43
\multicolbaselineskip=\skip44
\partial@page=\box27
\last@line=\box28
\mult@rightbox=\box29
\mult@grightbox=\box30
\mult@gfirstbox=\box31
\mult@firstbox=\box32
\@tempa=\box33
\@tempa=\box34
\@tempa=\box35
\@tempa=\box36
\@tempa=\box37
\@tempa=\box38
\@tempa=\box39
\@tempa=\box40
\@tempa=\box41
\@tempa=\box42
\@tempa=\box43
\@tempa=\box44
\@tempa=\box45
\@tempa=\box46
\@tempa=\box47
\@tempa=\box48
\@tempa=\box49
\c@columnbadness=\count93
\c@finalcolumnbadness=\count94
\last@try=\dimen108
\multicolovershoot=\dimen109
\multicolundershoot=\dimen110
\mult@nat@firstbox=\box50
\colbreak@box=\box51
)
\c@chapter=\count95
LaTeX Font Info:    Redeclaring math symbol \Gamma on input line 199.
LaTeX Font Info:    Redeclaring math symbol \Delta on input line 200.
LaTeX Font Info:    Redeclaring math symbol \Theta on input line 201.
LaTeX Font Info:    Redeclaring math symbol \Lambda on input line 202.
LaTeX Font Info:    Redeclaring math symbol \Xi on input line 203.
LaTeX Font Info:    Redeclaring math symbol \Pi on input line 204.
LaTeX Font Info:    Redeclaring math symbol \Sigma on input line 205.
LaTeX Font Info:    Redeclaring math symbol \Upsilon on input line 206.
LaTeX Font Info:    Redeclaring math symbol \Phi on input line 207.
LaTeX Font Info:    Redeclaring math symbol \Psi on input line 208.
LaTeX Font Info:    Redeclaring math symbol \Omega on input line 209.
\tocchpnum=\dimen111
\tocsecnum=\dimen112
\tocsectotal=\dimen113
\tocsubsecnum=\dimen114
\tocsubsectotal=\dimen115
\tocsubsubsecnum=\dimen116
\tocsubsubsectotal=\dimen117
\tocparanum=\dimen118
\tocparatotal=\dimen119
\tocsubparanum=\dimen120
\@tempcntc=\count96
\fnindent=\dimen121
\c@@inst=\count97
\c@@auth=\count98
\c@auco=\count99
\instindent=\dimen122
\authrun=\box52
\authorrunning=\toks14
\tocauthor=\toks15
\titrun=\box53
\titlerunning=\toks16
\toctitle=\toks17
\c@theorem=\count100
\c@case=\count101
\c@conjecture=\count102
\c@corollary=\count103
\c@definition=\count104
\c@example=\count105
\c@exercise=\count106
\c@lemma=\count107
\c@note=\count108
\c@problem=\count109
\c@property=\count110
\c@proposition=\count111
\c@question=\count112
\c@solution=\count113
\c@remark=\count114
\headlineindent=\dimen123
)
(/usr/share/texmf/tex/latex/base/latexsym.sty
Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols)
\symlasy=\mathgroup4
LaTeX Font Info:    Overwriting symbol font `lasy' in version `bold'
(Font)                  U/lasy/m/n --> U/lasy/b/n on input line 47.
)
(/usr/share/texmf/tex/latex/amsfonts/amssymb.sty
Package: amssymb 2002/01/22 v2.2d

(/usr/share/texmf/tex/latex/amsfonts/amsfonts.sty
Package: amsfonts 2001/10/25 v2.2f
\@emptytoks=\toks18
\symAMSa=\mathgroup5
\symAMSb=\mathgroup6
LaTeX Font Info:    Overwriting math alphabet `\mathfrak' in version `bold'
(Font)                  U/euf/m/n --> U/euf/b/n on input line 132.
))
\tempa=\box54
\tempb=\box55
\tempc=\dimen124
 (./main.aux)
\openout1 = `main.aux'.

LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 38.
LaTeX Font Info:    ... okay on input line 38.
LaTeX Font Info:    Try loading font information for U+lasy on input line 46.

(/usr/share/texmf/tex/latex/base/ulasy.fd
File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions
)
LaTeX Font Info:    Try loading font information for U+msa on input line 46.

(/usr/share/texmf/tex/latex/amsfonts/umsa.fd
File: umsa.fd 2002/01/19 v2.2g AMS font definitions
)
LaTeX Font Info:    Try loading font information for U+msb on input line 46.

(/usr/share/texmf/tex/latex/amsfonts/umsb.fd
File: umsb.fd 2002/01/19 v2.2g AMS font definitions
) [1

]
Underfull \vbox (badness 10000) has occurred while \output is active []

 [2]
Overfull \hbox (6.79999pt too wide) in paragraph at lines 245--335
[] 
 []

[3] [4]
Overfull \hbox (0.93633pt too wide) in paragraph at lines 401--410
[]\OT1/cmr/bx/n/10 (Equivalence). []\OT1/cmr/m/it/10 Let $\OMS/cmsy/m/n/10 R$ \
OT1/cmr/m/it/10 be a po-lar-ized rewrite sys-tem and $\OMS/cmsy/m/n/10 hR[]\OML
/cmm/m/it/10 ; \OMS/cmsy/m/n/10 Ti$
 []

[5]
Overfull \hbox (7.77724pt too wide) in paragraph at lines 518--526
\OT1/cmr/m/n/10 This the-ory does not have the cut elim-i-na-tion prop-erty as 
the se-quent $\OML/cmm/m/it/10 "\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x []H[]\OT1/c
mr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )) \OMS/cmsy/m/n/10 `
 []

[6]
Overfull \hbox (0.72232pt too wide) in paragraph at lines 541--550
[]\OT1/cmr/bx/n/10 (Clause, Con-straint, Uni-fier, Con-strained clause). \OT1/c
mr/m/it/10 A \OT1/cmr/m/n/10 clause
 []


Overfull \hbox (6.79999pt too wide) in paragraph at lines 595--616
[] 
 []

[7]
Overfull \hbox (6.79999pt too wide) in paragraph at lines 696--715
[] 
 []

[8] [9] [10]
Overfull \hbox (3.22523pt too wide) in paragraph at lines 934--938
[]\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 K$ \OT1/cmr/m/it/10 be a set of clause
s and $\OML/cmm/m/it/10 U$ \OT1/cmr/m/it/10 and $\OML/cmm/m/it/10 V$ \OT1/cmr/m
/it/10 two clauses. If $\OML/cmm/m/it/10 K; U ,[]\OMS/cmsy/m/n/10 ![]
 []

[11]
Underfull \hbox (badness 10000) in paragraph at lines 972--986
\OT1/cmr/m/n/10 has a smaller cut free proof. By Propo-si-tion 1[],
 []


Underfull \hbox (badness 7468) in paragraph at lines 1000--1036
\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 C[]\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; \OMS
/cmsy/m/n/10 j\OML/cmm/m/it/10 A[]\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; [] ; \OM
S/cmsy/m/n/10 j\OML/cmm/m/it/10 A[]\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; \OMS/cm
sy/m/n/10 :\OML/cmm/m/it/10 P[]; [] ; \OMS/cmsy/m/n/10 :\OML/cmm/m/it/10 P[] ,[
]\OMS/cmsy/m/n/10 ![] \U/lasy/m/n/10 2$ \OT1/cmr/m/n/10 and by Propo-si-tion 12
[],
 []


Underfull \hbox (badness 10000) in paragraph at lines 1000--1036
\OT1/cmr/m/n/10 thus, with the \OT1/cmr/bx/n/10 Con-ver-sion \OT1/cmr/m/n/10 an
d \OT1/cmr/bx/n/10 Re-duc-tion \OT1/cmr/m/n/10 rules,
 []


Underfull \hbox (badness 10000) in paragraph at lines 1037--1063
\OT1/cmr/m/n/10 thus, with the \OT1/cmr/bx/n/10 Con-ver-sion \OT1/cmr/m/n/10 an
d \OT1/cmr/bx/n/10 Re-duc-tion \OT1/cmr/m/n/10 rules,
 []


Underfull \hbox (badness 1622) in paragraph at lines 1065--1090
\OT1/cmr/m/n/10 propo-si-tions, say $\OML/cmm/m/it/10 A[]$\OT1/cmr/m/n/10 , re-
duces to a uni-ver-sal propo-si-tion $\OMS/cmsy/m/n/10 8\OML/cmm/m/it/10 x []B$
 \OT1/cmr/m/n/10 and
 []

[12]
Underfull \hbox (badness 10000) in paragraph at lines 1091--1111
\OT1/cmr/m/n/10 free proof of the same size, and, by in-duc-tion hy-poth-e-sis,

 []


Underfull \hbox (badness 10000) in paragraph at lines 1091--1111
\OT1/cmr/m/n/10 thus, with the \OT1/cmr/bx/n/10 Con-ver-sion \OT1/cmr/m/n/10 an
d \OT1/cmr/bx/n/10 Re-duc-tion \OT1/cmr/m/n/10 rules,
 []


Overfull \hbox (7.81352pt too wide) in paragraph at lines 1172--1178
[]\OT1/cmr/bx/n/10 (Soundness). []\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 U[]; [
] U[]$ \OT1/cmr/m/it/10 be clauses. If $\OML/cmm/m/it/10 U[]\OT1/cmr/m/n/10 [\U
/msb/m/n/10 ?\OT1/cmr/m/n/10 ]\OML/cmm/m/it/10 ; [] ; U[]\OT1/cmr/m/n/10 [\U/ms
b/m/n/10 ?\OT1/cmr/m/n/10 ] \OMS/cmsy/m/n/10 7![]
 []

[13]
Overfull \hbox (3.63283pt too wide) in paragraph at lines 1268--1274
[]\OT1/cmr/bx/n/10 (Completeness). []\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 U[]
; [] ; U[]$ \OT1/cmr/m/it/10 be clauses. If $\OML/cmm/m/it/10 U[]; [] ; U[] ,[]
\OMS/cmsy/m/n/10 ![]
 []

[14] [15] (./main.aux) ) 
Here is how much of TeX's memory you used:
 964 strings out of 256217
 10363 string characters out of 1917095
 74296 words of memory out of 1500000
 4279 multiletter control sequences out of 10000+200000
 11664 words of font info for 48 fonts, out of 1200000 for 2000
 645 hyphenation exceptions out of 8191
 29i,27n,24p,187b,286s stack positions out of 5000i,500n,6000p,200000b,15000s

Output written on main.dvi (15 pages, 79376 bytes).