Questionnaire-2024/sat_solvers_dpll/0053_sol.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{1|2|3|4|5}
		\dpllDecL{0|1|1|1|1}
		\dpllAssi{ - |$\lnot a$|$\lnot a, c$|$\lnot a, c, b$|\makecell{$\lnot a, c, b, $ \\ $\lnot d$}}
		\dpllClause{1}{$\lnot a, b, c$}{$\lnot a, b, c$|\done|\done|\done|\done}
		\dpllClause{2}{$a, c$}{$a, c$|$c$|\done|\done|\done}
		\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$b$|\done|\done}
		\dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$\lnot b, d$|$\lnot b, d$|$d$|\conflict}
		\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot d$|$\lnot d$|\done}
		\dpllClause{6}{$c, e$}{$c, e$|$c, e$|\done|\done|\done}
		\dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|\done|\done|\done}
		\dpllBCP{ - |$c$|$b$|$\lnot d$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{$\lnot a$| - | - | - | - }
	\end{dplltabular}
}

Conflict in step 5\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 1 -> 3
  \draw [->] (22.3bp,30.5bp) .. controls (35.47bp,30.5bp) and (58.583bp,30.5bp)  .. (85.878bp,30.5bp);
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  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,38.0bp) node {$$2$$};
  % Edge: 3 -> 4
  \draw [->] (107.97bp,32.873bp) .. controls (121.23bp,36.03bp) and (144.98bp,41.686bp)  .. (172.05bp,48.13bp);
  \draw (140.0bp,50.0bp) node {$$3$$};
  % Edge: 3 -> 6
  \draw [->] (107.07bp,25.696bp) .. controls (112.42bp,23.094bp) and (119.42bp,20.094bp)  .. (126.0bp,18.5bp) .. controls (152.72bp,12.025bp) and (184.6bp,10.902bp)  .. (215.0bp,11.119bp);
  \draw (140.0bp,26.0bp) node {$$5$$};
  % Edge: 4 -> 5
  \draw [->] (194.3bp,50.5bp) .. controls (207.47bp,50.5bp) and (230.58bp,50.5bp)  .. (257.88bp,50.5bp);
  \draw (226.0bp,58.0bp) node {$$4$$};
  % Edge: 5 -> 2
  \draw [->] (279.16bp,46.162bp) .. controls (287.01bp,42.445bp) and (298.56bp,36.972bp)  .. (317.68bp,27.917bp);
  % Edge: 6 -> 2
  \draw [->] (236.95bp,12.694bp) .. controls (253.12bp,14.634bp) and (285.4bp,18.508bp)  .. (316.79bp,22.275bp);
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (11.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
  \draw (11.0bp,30.5bp) node {$\lnot a$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (97.0bp,30.5bp) ellipse (11.0bp and 11.0bp);
  \draw (97.0bp,30.5bp) node {$c$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (328.0bp,23.5bp) ellipse (11.0bp and 11.0bp);
  \draw (328.0bp,23.5bp) node {$\bot$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (183.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
  \draw (183.0bp,50.5bp) node {$b$};
\end{scope}
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (226.0bp,11.5bp) ellipse (11.0bp and 11.0bp);
  \draw (226.0bp,11.5bp) node {$\lnot d$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (269.0bp,50.5bp) ellipse (11.0bp and 11.0bp);
  \draw (269.0bp,50.5bp) node {$d$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$4. \; \lnot b \lor d$}
	\AxiomC{$3. \; b \lor \lnot c$}
	\BinaryInfC{$d \lor \lnot c$}
	\AxiomC{$5. \; \lnot c \lor \lnot d$}
	\BinaryInfC{$\lnot c$}
	\AxiomC{$2. \; a \lor c$}
	\BinaryInfC{$a$}
\end{prooftree}

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{4}
		\dpllStep{6|7|8|9}
		\dpllDecL{0|0|1|1}
		\dpllAssi{ - |$a$|$a, \lnot b$|$a, \lnot b, \lnot c$}
		\dpllClause{1}{$\lnot a, b, c$}{$\lnot a, b, c$|$b, c$|$c$|\conflict}
		\dpllClause{2}{$a, c$}{$a, c$|\done|\done|\done}
		\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|$b, \lnot c$|$\lnot c$|\done}
		\dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$\lnot b, d$|\done|\done}
		\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c, \lnot d$|\done}
		\dpllClause{6}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$}
		\dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$}
		\dpllClause{8}{$a$}{$a$|\done|\done|\done}
		\dpllBCP{$a$| - |$\lnot c$| - }
		\dpllPL{ - | - | - | - }
		\dpllDeci{ - |$\lnot b$| - | - }
	\end{dplltabular}
}

Conflict in step 9\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 5
  \draw [->] (1.0536bp,87.0bp) .. controls (2.5071bp,87.0bp) and (33.188bp,87.0bp)  .. (64.696bp,87.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,94.5bp) node {$$8$$};
  % Edge: 1 -> 3
  \draw [->] (86.966bp,31.61bp) .. controls (100.23bp,35.083bp) and (123.98bp,41.304bp)  .. (151.05bp,48.393bp);
  \draw (119.0bp,51.5bp) node {$$1$$};
  % Edge: 1 -> 4
  \draw [->] (85.269bp,22.367bp) .. controls (90.57bp,18.542bp) and (97.789bp,14.087bp)  .. (105.0bp,12.0bp) .. controls (116.51bp,8.6691bp) and (129.91bp,8.3126bp)  .. (150.85bp,9.6198bp);
  \draw (119.0bp,19.5bp) node {$$3$$};
  % Edge: 3 -> 2
  \draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp)  .. (210.47bp,33.51bp);
  % Edge: 4 -> 2
  \draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp)  .. (210.09bp,26.697bp);
  % Edge: 5 -> 3
  \draw [->] (86.31bp,83.01bp) .. controls (99.682bp,77.279bp) and (124.62bp,66.591bp)  .. (151.65bp,55.008bp);
  \draw (119.0bp,81.5bp) node {$$1$$};
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,87.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,87.0bp) node {$a$};
\end{scope}
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,29.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,29.0bp) node {$\lnot b$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,51.0bp) node {$c$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,11.0bp) node {$\lnot c$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (221.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (221.0bp,30.0bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$1. \; \lnot a \lor b \lor c$}
	\AxiomC{$8. \; a$}
	\BinaryInfC{$b \lor c$}
	\AxiomC{$3. \; b \lor \lnot c$}
	\BinaryInfC{$b$}
\end{prooftree}