This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021) (preloaded format=pdflatex 2022.3.24) 30 NOV 2022 13:12 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. %&-line parsing enabled. **"/Users/shakilrafi/Padgett_Rafi/Scratch/Scratch for Lemma 32.tex" (/Users/shakilrafi/Padgett_Rafi/Scratch/Scratch for Lemma 32.tex LaTeX2e <2020-10-01> patch level 4 L3 programming layer <2021-02-18> (/usr/local/texlive/2021/texmf-dist/tex/latex/base/article.cls Document Class: article 2020/04/10 v1.4m Standard LaTeX document class (/usr/local/texlive/2021/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2020/04/10 v1.4m Standard LaTeX file (size option) ) \c@part=\count179 \c@section=\count180 \c@subsection=\count181 \c@subsubsection=\count182 \c@paragraph=\count183 \c@subparagraph=\count184 \c@figure=\count185 \c@table=\count186 \abovecaptionskip=\skip47 \belowcaptionskip=\skip48 \bibindent=\dimen138 ) (/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsmath.sty Package: amsmath 2020/09/23 v2.17i AMS math features \@mathmargin=\skip49 For additional information on amsmath, use the `?' option. (/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 AMS text (/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 generic functions \@emptytoks=\toks15 \ex@=\dimen139 )) (/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d Bold Symbols \pmbraise@=\dimen140 ) (/usr/local/texlive/2021/texmf-dist/tex/latex/amsmath/amsopn.sty Package: amsopn 2016/03/08 v2.02 operator names ) \inf@bad=\count187 LaTeX Info: Redefining \frac on input line 234. \uproot@=\count188 \leftroot@=\count189 LaTeX Info: Redefining \overline on input line 399. \classnum@=\count190 \DOTSCASE@=\count191 LaTeX Info: Redefining \ldots on input line 496. LaTeX Info: Redefining \dots on input line 499. LaTeX Info: Redefining \cdots on input line 620. \Mathstrutbox@=\box47 \strutbox@=\box48 \big@size=\dimen141 LaTeX Font Info: Redeclaring font encoding OML on input line 743. LaTeX Font Info: Redeclaring font encoding OMS on input line 744. \macc@depth=\count192 \c@MaxMatrixCols=\count193 \dotsspace@=\muskip16 \c@parentequation=\count194 \dspbrk@lvl=\count195 \tag@help=\toks16 \row@=\count196 \column@=\count197 \maxfields@=\count198 \andhelp@=\toks17 \eqnshift@=\dimen142 \alignsep@=\dimen143 \tagshift@=\dimen144 \tagwidth@=\dimen145 \totwidth@=\dimen146 \lineht@=\dimen147 \@envbody=\toks18 \multlinegap=\skip50 \multlinetaggap=\skip51 \mathdisplay@stack=\toks19 LaTeX Info: Redefining \[ on input line 2923. LaTeX Info: Redefining \] on input line 2924. ) (/usr/local/texlive/2021/texmf-dist/tex/latex/amscls/amsthm.sty Package: amsthm 2020/05/29 v2.20.6 \thm@style=\toks20 \thm@bodyfont=\toks21 \thm@headfont=\toks22 \thm@notefont=\toks23 \thm@headpunct=\toks24 \thm@preskip=\skip52 \thm@postskip=\skip53 \thm@headsep=\skip54 \dth@everypar=\toks25 ) (/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/amssymb.sty Package: amssymb 2013/01/14 v3.01 AMS font symbols (/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Redeclaring math symbol \hbar on input line 98. LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 106. )) (/usr/local/texlive/2021/texmf-dist/tex/latex/geometry/geometry.sty Package: geometry 2020/01/02 v5.9 Page Geometry (/usr/local/texlive/2021/texmf-dist/tex/latex/graphics/keyval.sty Package: keyval 2014/10/28 v1.15 key=value parser (DPC) \KV@toks@=\toks26 ) (/usr/local/texlive/2021/texmf-dist/tex/generic/iftex/ifvtex.sty Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead. (/usr/local/texlive/2021/texmf-dist/tex/generic/iftex/iftex.sty Package: iftex 2020/03/06 v1.0d TeX engine tests )) \Gm@cnth=\count199 \Gm@cntv=\count266 \c@Gm@tempcnt=\count267 \Gm@bindingoffset=\dimen148 \Gm@wd@mp=\dimen149 \Gm@odd@mp=\dimen150 \Gm@even@mp=\dimen151 \Gm@layoutwidth=\dimen152 \Gm@layoutheight=\dimen153 \Gm@layouthoffset=\dimen154 \Gm@layoutvoffset=\dimen155 \Gm@dimlist=\toks27 ) (/usr/local/texlive/2021/texmf-dist/tex/generic/soul/soul.sty Package: soul 2003/11/17 v2.4 letterspacing/underlining (mf) \SOUL@word=\toks28 \SOUL@lasttoken=\toks29 \SOUL@cmds=\toks30 \SOUL@buffer=\toks31 \SOUL@token=\toks32 \SOUL@spaceskip=\skip55 \SOUL@ttwidth=\dimen156 \SOUL@uldp=\dimen157 \SOUL@ulht=\dimen158 ) (/usr/local/texlive/2021/texmf-dist/tex/latex/bbm-macros/bbm.sty Package: bbm 1999/03/15 V 1.2 provides fonts for set symbols - TH LaTeX Font Info: Overwriting math alphabet `\mathbbm' in version `bold' (Font) U/bbm/m/n --> U/bbm/bx/n on input line 33. LaTeX Font Info: Overwriting math alphabet `\mathbbmss' in version `bold' (Font) U/bbmss/m/n --> U/bbmss/bx/n on input line 35. ) (/usr/local/texlive/2021/texmf-dist/tex/latex/cancel/cancel.sty Package: cancel 2013/04/12 v2.2 Cancel math terms ) (/usr/local/texlive/2021/texmf-dist/tex/latex/xcolor/xcolor.sty Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK) (/usr/local/texlive/2021/texmf-dist/tex/latex/graphics-cfg/color.cfg File: color.cfg 2016/01/02 v1.6 sample color configuration ) Package xcolor Info: Driver file: pdftex.def on input line 225. (/usr/local/texlive/2021/texmf-dist/tex/latex/graphics-def/pdftex.def File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex ) Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348. Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352. Package xcolor Info: Model `RGB' extended on input line 1364. Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366. Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367. Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368. Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369. Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370. Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371. ) (/usr/local/texlive/2021/texmf-dist/tex/latex/enumitem/enumitem.sty Package: enumitem 2019/06/20 v3.9 Customized lists \labelindent=\skip56 \enit@outerparindent=\dimen159 \enit@toks=\toks33 \enit@inbox=\box49 \enit@count@id=\count268 \enitdp@description=\count269 ) (/usr/local/texlive/2021/texmf-dist/tex/latex/jknapltx/mathrsfs.sty Package: mathrsfs 1996/01/01 Math RSFS package v1.0 (jk) \symrsfs=\mathgroup6 ) \c@theorem=\count270 \c@corollary=\count271 (/usr/local/texlive/2021/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def File: l3backend-pdftex.def 2021-03-18 L3 backend support: PDF output (pdfTeX) \l__color_backend_stack_int=\count272 \l__pdf_internal_box=\box50 ) (/Users/shakilrafi/Padgett_Rafi/Scratch/Scratch for Lemma 32.aux) \openout1 = `"Scratch for Lemma 32.aux"'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 35. LaTeX Font Info: ... okay on input line 35. *geometry* driver: auto-detecting *geometry* detected driver: pdftex *geometry* verbose mode - [ preamble ] result: * driver: pdftex * paper: a4paper * layout: * layoutoffset:(h,v)=(0.0pt,0.0pt) * modes: * h-part:(L,W,R)=(81.94394pt, 433.62pt, 81.94394pt) * v-part:(T,H,B)=(106.75473pt, 578.15999pt, 160.13213pt) * \paperwidth=597.50787pt * \paperheight=845.04684pt * \textwidth=433.62pt * \textheight=578.15999pt * \oddsidemargin=9.67395pt * \evensidemargin=9.67395pt * \topmargin=-2.51526pt * \headheight=12.0pt * \headsep=25.0pt * \topskip=10.0pt * \footskip=30.0pt * \marginparwidth=65.0pt * \marginparsep=11.0pt * \columnsep=10.0pt * \skip\footins=9.0pt plus 4.0pt minus 2.0pt * \hoffset=0.0pt * \voffset=0.0pt * \mag=1000 * \@twocolumnfalse * \@twosidefalse * \@mparswitchfalse * \@reversemarginfalse * (1in=72.27pt=25.4mm, 1cm=28.453pt) (/usr/local/texlive/2021/texmf-dist/tex/context/base/mkii/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] \scratchcounter=\count273 \scratchdimen=\dimen160 \scratchbox=\box51 \nofMPsegments=\count274 \nofMParguments=\count275 \everyMPshowfont=\toks34 \MPscratchCnt=\count276 \MPscratchDim=\dimen161 \MPnumerator=\count277 \makeMPintoPDFobject=\count278 \everyMPtoPDFconversion=\toks35 ) LaTeX Font Info: Trying to load font information for U+msa on input line 36. (/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/umsa.fd File: umsa.fd 2013/01/14 v3.01 AMS symbols A ) LaTeX Font Info: Trying to load font information for U+msb on input line 36. (/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) LaTeX Font Info: Trying to load font information for U+rsfs on input line 36. (/usr/local/texlive/2021/texmf-dist/tex/latex/jknapltx/ursfs.fd File: ursfs.fd 1998/03/24 rsfs font definition file (jk) ) [1 {/usr/local/texlive/2021/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (/Users/shakilrafi/Padgett_Rafi/Scratch/Scratch for Lemma 32.aux) ) Here is how much of TeX's memory you used: 3697 strings out of 478994 50033 string characters out of 5858184 347435 words of memory out of 5000000 21157 multiletter control sequences out of 15000+600000 409181 words of font info for 50 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 68i,6n,74p,278b,214s stack positions out of 5000i,500n,10000p,200000b,80000s Output written on "/Users/shakilrafi/Padgett_Rafi/Scratch/Scratch for Lemma 32.pdf" (1 page, 28957 bytes). PDF statistics: 20 PDF objects out of 1000 (max. 8388607) 13 compressed objects within 1 object stream 0 named destinations out of 1000 (max. 500000) 1 words of extra memory for PDF output out of 10000 (max. 10000000)