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5.2 KiB

\hspace{-0.09cm}\scalebox{0.85}{
\begin{dplltabular}{4}
\dpllStep{1|2|3|4}
\dpllDecL{0|0|1|1}
\dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, e$}
\dpllClause{1}{$\lnot a, d$}{$\lnot a, d$|\done|\done|\done}
\dpllClause{2}{$\lnot d, c, \lnot a$}{$\lnot d, c, \lnot a$|\done|\done|\done}
\dpllClause{3}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$e$|\done}
\dpllClause{4}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|$\lnot b, \lnot e$|$\lnot e$|\conflict}
\dpllClause{5}{$b, f$}{$b, f$|$b, f$|\done|\done}
\dpllClause{6}{$b, \lnot f$}{$b, \lnot f$|$b, \lnot f$|\done|\done}
\dpllBCP{ - | - |$e$| - }
\dpllPL{$\lnot a$| - | - | - }
\dpllDeci{ - |$b$| - | - }
\end{dplltabular}
}
Conflict in step 4\\
\scalebox{0.75}{
\begin{tikzpicture}[>=latex,line join=bevel,]
\pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
% Edge: 1 -> 3
\draw [->] (21.966bp,33.373bp) .. controls (35.227bp,36.53bp) and (58.98bp,42.186bp) .. (86.047bp,48.63bp);
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (54.0bp,50.5bp) node {$$3$$};
% Edge: 1 -> 4
\draw [->] (21.111bp,26.371bp) .. controls (26.482bp,23.828bp) and (33.482bp,20.828bp) .. (40.0bp,19.0bp) .. controls (51.65bp,15.733bp) and (65.057bp,13.758bp) .. (85.923bp,11.639bp);
\draw (54.0bp,26.5bp) node {$$4$$};
% Edge: 3 -> 2
\draw [->] (107.67bp,47.438bp) .. controls (115.41bp,44.585bp) and (126.51bp,40.495bp) .. (145.47bp,33.51bp);
% Edge: 4 -> 2
\draw [->] (107.67bp,14.223bp) .. controls (115.24bp,16.746bp) and (126.02bp,20.339bp) .. (145.09bp,26.697bp);
% Node: 1
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (11.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
\draw (11.0bp,31.0bp) node {$b$};
\end{scope}
% Node: 3
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (97.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
\draw (97.0bp,51.0bp) node {$e$};
\end{scope}
% Node: 4
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (97.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
\draw (97.0bp,11.0bp) node {$\lnot e$};
\end{scope}
% Node: 2
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (156.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
\draw (156.0bp,30.0bp) node {$\bot$};
\end{scope}
%
\end{tikzpicture}
}
\begin{prooftree}
\AxiomC{$3. \; \lnot b \lor e$}
\AxiomC{$4. \; \lnot b \lor \lnot e$}
\BinaryInfC{$\lnot b$}
\end{prooftree}
\hspace{-0.09cm}\scalebox{0.85}{
\begin{dplltabular}{3}
\dpllStep{5|6|7}
\dpllDecL{0|0|0}
\dpllAssi{$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, f$}
\dpllClause{1}{$\lnot a, d$}{\done|\done|\done}
\dpllClause{2}{$\lnot d, c, \lnot a$}{\done|\done|\done}
\dpllClause{3}{$\lnot b, e$}{$\lnot b, e$|\done|\done}
\dpllClause{4}{$\lnot b, \lnot e$}{$\lnot b, \lnot e$|\done|\done}
\dpllClause{5}{$b, f$}{$b, f$|$f$|\done}
\dpllClause{6}{$b, \lnot f$}{$b, \lnot f$|$\lnot f$|\conflict}
\dpllClause{7}{$\lnot b$}{$\lnot b$|\done|\done}
\dpllBCP{$\lnot b$|$f$| - }
\dpllPL{ - | - | - }
\dpllDeci{ - | - |UNSAT}
\end{dplltabular}
}
Conflict in step 7\\
\scalebox{0.75}{
\begin{tikzpicture}[>=latex,line join=bevel,]
\pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
% Edge: 0 -> 4
\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 {$$7$$};
% Edge: 2 -> 1
\draw [->] (172.67bp,47.438bp) .. controls (180.41bp,44.585bp) and (191.51bp,40.495bp) .. (210.47bp,33.51bp);
% Edge: 3 -> 1
\draw [->] (172.67bp,14.223bp) .. controls (180.24bp,16.746bp) and (191.02bp,20.339bp) .. (210.09bp,26.697bp);
% Edge: 4 -> 2
\draw [->] (86.966bp,33.373bp) .. controls (100.23bp,36.53bp) and (123.98bp,42.186bp) .. (151.05bp,48.63bp);
\draw (119.0bp,50.5bp) node {$$5$$};
% Edge: 4 -> 3
\draw [->] (86.111bp,26.371bp) .. controls (91.482bp,23.828bp) and (98.482bp,20.828bp) .. (105.0bp,19.0bp) .. controls (116.65bp,15.733bp) and (130.06bp,13.758bp) .. (150.92bp,11.639bp);
\draw (119.0bp,26.5bp) node {$$6$$};
% Node: 4
\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 {$\lnot b$};
\end{scope}
% Node: 1
\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}
% Node: 2
\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 {$f$};
\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 {$\lnot f$};
\end{scope}
%
\end{tikzpicture}
}
\begin{prooftree}
\AxiomC{$5. \; b \lor f$}
\AxiomC{$6. \; b \lor \lnot f$}
\BinaryInfC{$b$}
\AxiomC{$7. \; \lnot b$}
\BinaryInfC{$\bot$}
\end{prooftree}