Questionnaire-2024/sat_solvers_dpll/0049_sol_second_part.tex

\hspace{-0.09cm}\scalebox{0.85}{
	\begin{dplltabular}{5}
		\dpllStep{12|13|14|15|16}
		\dpllDecL{0|0|0|0|0}
		\dpllAssi{ - |$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $\lnot d$}}
		\dpllClause{1}{$\lnot a, \lnot d$}{$\lnot a, \lnot d$|$\lnot d$|$\lnot d$|$\lnot d$|\done}
		\dpllClause{2}{$a, b, c$}{$a, b, c$|\done|\done|\done|\done}
		\dpllClause{3}{$\lnot a, b$}{$\lnot a, b$|$b$|\done|\done|\done}
		\dpllClause{4}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done}
		\dpllClause{5}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\conflict}
		\dpllClause{6}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$}
		\dpllClause{7}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|\done}
		\dpllClause{8}{$a, b$}{$a, b$|\done|\done|\done|\done}
		\dpllClause{9}{$a$}{$a$|\done|\done|\done|\done}
		\dpllBCP{$a$|$b$|$c$|$\lnot d$| - }
		\dpllPL{ - | - | - | - | - }
		\dpllDeci{ - | - | - | - |UNSAT}
	\end{dplltabular}
}

Conflict in step 16\\
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: 0 -> 6
  \draw [->] (1.0536bp,31.0bp) .. controls (2.5071bp,31.0bp) and (33.188bp,31.0bp)  .. (64.696bp,31.0bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (33.0bp,38.5bp) node {$$9$$};
  % Edge: 2 -> 1
  \draw [->] (216.0bp,49.131bp) .. controls (240.99bp,46.927bp) and (308.17bp,40.812bp)  .. (364.0bp,34.0bp) .. controls (366.51bp,33.694bp) and (369.14bp,33.349bp)  .. (381.9bp,31.544bp);
  % Edge: 3 -> 4
  \draw [->] (173.3bp,11.0bp) .. controls (186.47bp,11.0bp) and (209.58bp,11.0bp)  .. (236.88bp,11.0bp);
  \draw (205.0bp,18.5bp) node {$$4$$};
  % Edge: 4 -> 5
  \draw [->] (259.3bp,11.0bp) .. controls (272.47bp,11.0bp) and (295.58bp,11.0bp)  .. (322.88bp,11.0bp);
  \draw (291.0bp,18.5bp) node {$$5$$};
  % Edge: 5 -> 1
  \draw [->] (344.67bp,14.223bp) .. controls (352.24bp,16.746bp) and (363.02bp,20.339bp)  .. (382.09bp,26.697bp);
  % Edge: 6 -> 2
  \draw [->] (86.965bp,32.491bp) .. controls (107.83bp,35.613bp) and (156.46bp,42.888bp)  .. (194.08bp,48.516bp);
  \draw (119.0bp,46.5bp) node {$$1$$};
  % Edge: 6 -> 3
  \draw [->] (85.22bp,24.026bp) .. controls (90.504bp,19.994bp) and (97.72bp,15.28bp)  .. (105.0bp,13.0bp) .. controls (116.44bp,9.4177bp) and (129.84bp,8.8202bp)  .. (150.82bp,9.7781bp);
  \draw (119.0bp,20.5bp) node {$$3$$};
  % Node: 6
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (76.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
  \draw (76.0bp,31.0bp) node {$a$};
\end{scope}
  % Node: 1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (393.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
  \draw (393.0bp,30.0bp) node {$\bot$};
\end{scope}
  % Node: 2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (205.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
  \draw (205.0bp,50.0bp) node {$\lnot d$};
\end{scope}
  % Node: 3
\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 {$b$};
\end{scope}
  % Node: 4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (248.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (248.0bp,11.0bp) node {$c$};
\end{scope}
  % Node: 5
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (334.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
  \draw (334.0bp,11.0bp) node {$d$};
\end{scope}
%
\end{tikzpicture}


}
\begin{prooftree}
	\AxiomC{$5. \; \lnot c \lor d$}
	\AxiomC{$4. \; \lnot b \lor c$}
	\BinaryInfC{$d \lor \lnot b$}
	\AxiomC{$1. \; \lnot a \lor \lnot d$}
	\BinaryInfC{$\lnot b \lor \lnot a$}
	\AxiomC{$3. \; \lnot a \lor b$}
	\BinaryInfC{$\lnot a$}
	\AxiomC{$9. \; a$}
	\BinaryInfC{$\bot$}
\end{prooftree}