Questionnaire-2024/sat_solvers_dpll/0035_sol.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{1|2|3|4|5}
		\dpllDecL{0|1|1|1|1}
		\dpllAssi{ - |$\lnot a$|$\lnot a, \lnot d$|$\lnot a, \lnot d, b$|\makecell{$\lnot a, \lnot d, b, $ \\ $\lnot c$}}
		\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$b$|\done|\done}
		\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done}
		\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|$\lnot d$|\done|\done|\done}
		\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$\lnot b, c$|$c$|\conflict}
		\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c$|$\lnot c$|\done}
		\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|\done}
		\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done|\done|\done}
		\dpllBCP{ - |$\lnot d$|$b$|$\lnot c$| - }
		\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 -> 4
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  \pgfsetstrokecolor{strokecol}
  \draw (54.0bp,38.0bp) node {$$3$$};
  % Edge: 3 -> 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: 4 -> 3
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  \draw (140.0bp,50.0bp) node {$$1$$};
  % Edge: 4 -> 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: 5 -> 2
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  % 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: 4
\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 {$\lnot d$};
\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: 3
\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: 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 {$c$};
\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 {$\lnot c$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$4. \; \lnot b \lor c$}
	\AxiomC{$1. \; b \lor d$}
	\BinaryInfC{$c \lor d$}
	\AxiomC{$5. \; \lnot c \lor d$}
	\BinaryInfC{$d$}
	\AxiomC{$3. \; a \lor \lnot d$}
	\BinaryInfC{$a$}
\end{prooftree}

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{6|7|8|9|10}
		\dpllDecL{0|0|0|0|0}
		\dpllAssi{ - |$a$|$a, c$|$a, c, d$|\makecell{$a, c, d, $ \\ $\lnot e$}}
		\dpllClause{1}{$b, d$}{$b, d$|$b, d$|$b, d$|\done|\done}
		\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
		\dpllClause{3}{$a, \lnot d$}{$a, \lnot d$|\done|\done|\done|\done}
		\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|\done|\done|\done}
		\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$d$|\done|\done}
		\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
		\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
		\dpllClause{8}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$c$|$d$|$\lnot e$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |UNSAT}
	\end{dplltabular}
}

Conflict in step 10\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 6
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  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,37.5bp) node {$$8$$};
  % Edge: 2 -> 3
  \draw [->] (172.97bp,32.373bp) .. controls (186.23bp,35.53bp) and (209.98bp,41.186bp)  .. (237.05bp,47.63bp);
  \draw (205.0bp,49.5bp) node {$$5$$};
  % Edge: 2 -> 4
  \draw [->] (172.07bp,25.196bp) .. controls (177.42bp,22.594bp) and (184.42bp,19.594bp)  .. (191.0bp,18.0bp) .. controls (217.72bp,11.525bp) and (249.6bp,10.402bp)  .. (280.0bp,10.619bp);
  \draw (205.0bp,25.5bp) node {$$6$$};
  % Edge: 3 -> 5
  \draw [->] (259.3bp,50.0bp) .. controls (272.47bp,50.0bp) and (295.58bp,50.0bp)  .. (322.88bp,50.0bp);
  \draw (291.0bp,57.5bp) node {$$7$$};
  % Edge: 4 -> 1
  \draw [->] (301.95bp,12.194bp) .. controls (318.12bp,14.134bp) and (350.4bp,18.008bp)  .. (381.79bp,21.775bp);
  % Edge: 5 -> 1
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  % Edge: 6 -> 2
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  \draw (119.0bp,37.5bp) node {$$2$$};
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,30.0bp) node {$a$};
\end{scope}
  % Node: 1
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (393.0bp,23.0bp) ellipse (11.0bp and 11.0bp);
  \draw (393.0bp,23.0bp) node {$\bot$};
\end{scope}
  % Node: 2
\begin{scope}
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  \pgfsetstrokecolor{strokecol}
  \draw (162.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (162.0bp,30.0bp) node {$c$};
\end{scope}
  % Node: 3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (248.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
  \draw (248.0bp,50.0bp) node {$d$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (291.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (291.0bp,11.0bp) node {$e$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (334.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
  \draw (334.0bp,50.0bp) node {$\lnot e$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$7. \; \lnot d \lor \lnot e$}
	\AxiomC{$5. \; \lnot c \lor d$}
	\BinaryInfC{$\lnot e \lor \lnot c$}
	\AxiomC{$6. \; \lnot c \lor e$}
	\BinaryInfC{$\lnot c$}
	\AxiomC{$2. \; \lnot a \lor c$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$8. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}