You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
107 lines
3.8 KiB
107 lines
3.8 KiB
\hspace{-0.09cm}\scalebox{0.85}{
|
|
\begin{dplltabular}{5}
|
|
\dpllStep{10|11|12|13|14}
|
|
\dpllDecL{0|0|0|0|0}
|
|
\dpllAssi{$a$|$a, b$|$a, b, d$|\makecell{$a, b, d, $ \\ $\lnot c$}|\makecell{$a, b, d, $ \\ $\lnot c, \lnot e$}}
|
|
\dpllClause{1}{$\lnot a, b, c$}{$b, c$|\done|\done|\done|\done}
|
|
\dpllClause{2}{$a, c$}{\done|\done|\done|\done|\done}
|
|
\dpllClause{3}{$b, \lnot c$}{$b, \lnot c$|\done|\done|\done|\done}
|
|
\dpllClause{4}{$\lnot b, d$}{$\lnot b, d$|$d$|\done|\done|\done}
|
|
\dpllClause{5}{$\lnot c, \lnot d$}{$\lnot c, \lnot d$|$\lnot c, \lnot d$|$\lnot c$|\done|\done}
|
|
\dpllClause{6}{$c, e$}{$c, e$|$c, e$|$c, e$|$e$|\conflict}
|
|
\dpllClause{7}{$c, \lnot e$}{$c, \lnot e$|$c, \lnot e$|$c, \lnot e$|$\lnot e$|\done}
|
|
\dpllClause{8}{$a$}{\done|\done|\done|\done|\done}
|
|
\dpllClause{9}{$b$}{$b$|\done|\done|\done|\done}
|
|
\dpllBCP{$b$|$d$|$\lnot c$|$\lnot e$| - }
|
|
\dpllPL{ - | - | - | - | - }
|
|
\dpllDeci{ - | - | - | - |UNSAT}
|
|
\end{dplltabular}
|
|
}
|
|
|
|
Conflict in step 14\\
|
|
\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 -> 3
|
|
\draw [->] (173.3bp,31.0bp) .. controls (186.47bp,31.0bp) and (209.58bp,31.0bp) .. (236.88bp,31.0bp);
|
|
\draw (205.0bp,38.5bp) node {$$5$$};
|
|
% Edge: 3 -> 4
|
|
\draw [->] (258.97bp,33.373bp) .. controls (272.23bp,36.53bp) and (295.98bp,42.186bp) .. (323.05bp,48.63bp);
|
|
\draw (291.0bp,50.5bp) node {$$6$$};
|
|
% Edge: 3 -> 5
|
|
\draw [->] (258.11bp,26.371bp) .. controls (263.48bp,23.828bp) and (270.48bp,20.828bp) .. (277.0bp,19.0bp) .. controls (288.65bp,15.733bp) and (302.06bp,13.758bp) .. (322.92bp,11.639bp);
|
|
\draw (291.0bp,26.5bp) node {$$7$$};
|
|
% Edge: 4 -> 1
|
|
\draw [->] (344.67bp,47.438bp) .. controls (352.41bp,44.585bp) and (363.51bp,40.495bp) .. (382.47bp,33.51bp);
|
|
% 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 [->] (87.3bp,31.0bp) .. controls (100.47bp,31.0bp) and (123.58bp,31.0bp) .. (150.88bp,31.0bp);
|
|
\draw (119.0bp,38.5bp) node {$$4$$};
|
|
% 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 {$b$};
|
|
\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 (162.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (162.0bp,31.0bp) node {$d$};
|
|
\end{scope}
|
|
% Node: 3
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (248.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (248.0bp,31.0bp) node {$\lnot c$};
|
|
\end{scope}
|
|
% Node: 4
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (334.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (334.0bp,51.0bp) node {$e$};
|
|
\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 {$\lnot e$};
|
|
\end{scope}
|
|
%
|
|
\end{tikzpicture}
|
|
|
|
|
|
}
|
|
\begin{prooftree}
|
|
\AxiomC{$6. \; c \lor e$}
|
|
\AxiomC{$7. \; c \lor \lnot e$}
|
|
\BinaryInfC{$c$}
|
|
\AxiomC{$5. \; \lnot c \lor \lnot d$}
|
|
\BinaryInfC{$\lnot d$}
|
|
\AxiomC{$4. \; \lnot b \lor d$}
|
|
\BinaryInfC{$\lnot b$}
|
|
\AxiomC{$9. \; b$}
|
|
\BinaryInfC{$\bot$}
|
|
\end{prooftree}
|
|
|