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.
147 lines
6.1 KiB
147 lines
6.1 KiB
\hspace{-0.09cm}\scalebox{0.85}{
|
|
\begin{dplltabular}{7}
|
|
\dpllStep{1|2|3|4|5|6|7}
|
|
\dpllDecL{0|1|1|1|1|1|1}
|
|
\dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, \lnot c$|\makecell{$\lnot a, b, \lnot c, $ \\ $d$}|\makecell{$\lnot a, b, \lnot c, $ \\ $d, e$}|\makecell{$\lnot a, b, \lnot c, $ \\ $d, e, \lnot f$}}
|
|
\dpllClause{1}{$a, b$}{$a, b$|$b$|\done|\done|\done|\done|\done}
|
|
\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done|\done|\done}
|
|
\dpllClause{3}{$c, d$}{$c, d$|$c, d$|$c, d$|$d$|\done|\done|\done}
|
|
\dpllClause{4}{$\lnot b, \lnot c$}{$\lnot b, \lnot c$|$\lnot b, \lnot c$|$\lnot c$|\done|\done|\done|\done}
|
|
\dpllClause{5}{$d, e$}{$d, e$|$d, e$|$d, e$|$d, e$|\done|\done|\done}
|
|
\dpllClause{6}{$\lnot e, f$}{$\lnot e, f$|$\lnot e, f$|$\lnot e, f$|$\lnot e, f$|$\lnot e, f$|$f$|\conflict}
|
|
\dpllClause{7}{$\lnot d, \lnot f$}{$\lnot d, \lnot f$|$\lnot d, \lnot f$|$\lnot d, \lnot f$|$\lnot d, \lnot f$|$\lnot f$|$\lnot f$|\done}
|
|
\dpllClause{8}{$b, \lnot f$}{$b, \lnot f$|$b, \lnot f$|\done|\done|\done|\done|\done}
|
|
\dpllClause{9}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$e$|$e$|$e$|\done|\done}
|
|
\dpllBCP{ - |$b$|$\lnot c$|$d$|$e$|$\lnot f$| - }
|
|
\dpllPL{ - | - | - | - | - | - | - }
|
|
\dpllDeci{$\lnot a$| - | - | - | - | - | - }
|
|
\end{dplltabular}
|
|
}
|
|
|
|
Conflict in step 7\\
|
|
\scalebox{0.75}{
|
|
|
|
\begin{tikzpicture}[>=latex,line join=bevel,]
|
|
\pgfsetlinewidth{1bp}
|
|
%%
|
|
\pgfsetcolor{black}
|
|
% Edge: 1 -> 3
|
|
\draw [->] (22.3bp,31.0bp) .. controls (35.47bp,31.0bp) and (58.583bp,31.0bp) .. (85.878bp,31.0bp);
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (54.0bp,38.5bp) node {$$1$$};
|
|
% Edge: 3 -> 5
|
|
\draw [->] (107.97bp,33.373bp) .. controls (121.23bp,36.53bp) and (144.98bp,42.186bp) .. (172.05bp,48.63bp);
|
|
\draw (140.0bp,50.5bp) node {$$4$$};
|
|
% Edge: 3 -> 8
|
|
\draw [->] (107.11bp,26.371bp) .. controls (112.48bp,23.828bp) and (119.48bp,20.828bp) .. (126.0bp,19.0bp) .. controls (137.65bp,15.733bp) and (151.06bp,13.758bp) .. (171.92bp,11.639bp);
|
|
\draw (140.0bp,26.5bp) node {$$9$$};
|
|
% Edge: 4 -> 7
|
|
\draw [->] (280.3bp,50.0bp) .. controls (293.47bp,50.0bp) and (316.58bp,50.0bp) .. (343.88bp,50.0bp);
|
|
\draw (312.0bp,57.5bp) node {$$7$$};
|
|
% Edge: 5 -> 4
|
|
\draw [->] (194.3bp,50.877bp) .. controls (207.47bp,50.721bp) and (230.58bp,50.445bp) .. (257.88bp,50.12bp);
|
|
\draw (226.0bp,57.5bp) node {$$3$$};
|
|
% Edge: 6 -> 2
|
|
\draw [->] (322.95bp,12.194bp) .. controls (339.12bp,14.134bp) and (371.4bp,18.008bp) .. (402.79bp,21.775bp);
|
|
% Edge: 7 -> 2
|
|
\draw [->] (365.16bp,45.662bp) .. controls (373.01bp,41.945bp) and (384.56bp,36.472bp) .. (403.68bp,27.417bp);
|
|
% Edge: 8 -> 6
|
|
\draw [->] (194.39bp,11.0bp) .. controls (215.43bp,11.0bp) and (263.37bp,11.0bp) .. (300.82bp,11.0bp);
|
|
\draw (226.0bp,18.5bp) node {$$6$$};
|
|
% 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 {$\lnot a$};
|
|
\end{scope}
|
|
% Node: 3
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (97.0bp,31.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (97.0bp,31.0bp) node {$b$};
|
|
\end{scope}
|
|
% Node: 2
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (414.0bp,23.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (414.0bp,23.0bp) node {$\bot$};
|
|
\end{scope}
|
|
% Node: 5
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (183.0bp,51.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (183.0bp,51.0bp) node {$\lnot c$};
|
|
\end{scope}
|
|
% Node: 8
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (183.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (183.0bp,11.0bp) node {$e$};
|
|
\end{scope}
|
|
% Node: 4
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (269.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (269.0bp,50.0bp) node {$d$};
|
|
\end{scope}
|
|
% Node: 7
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (355.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (355.0bp,50.0bp) node {$\lnot f$};
|
|
\end{scope}
|
|
% Node: 6
|
|
\begin{scope}
|
|
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
|
|
\pgfsetstrokecolor{strokecol}
|
|
\draw (312.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
|
|
\draw (312.0bp,11.0bp) node {$f$};
|
|
\end{scope}
|
|
%
|
|
\end{tikzpicture}
|
|
|
|
|
|
}
|
|
\begin{prooftree}
|
|
\AxiomC{$6. \; \lnot e \lor f$}
|
|
\AxiomC{$7. \; \lnot d \lor \lnot f$}
|
|
\BinaryInfC{$\lnot e \lor \lnot d$}
|
|
\AxiomC{$3. \; c \lor d$}
|
|
\BinaryInfC{$\lnot e \lor c$}
|
|
\AxiomC{$4. \; \lnot b \lor \lnot c$}
|
|
\BinaryInfC{$\lnot e \lor \lnot b$}
|
|
\AxiomC{$9. \; \lnot b \lor e$}
|
|
\BinaryInfC{$\lnot b$}
|
|
\AxiomC{$1. \; a \lor b$}
|
|
\BinaryInfC{$a$}
|
|
\end{prooftree}
|
|
|
|
\hspace{-0.09cm}\scalebox{0.85}{
|
|
\begin{dplltabular}{7}
|
|
\dpllStep{8|9|10|11|12|13|14}
|
|
\dpllDecL{0|0|0|0|0|0|0}
|
|
\dpllAssi{ - |$a$|$a, c$|$a, c, \lnot b$|\makecell{$a, c, \lnot b, $ \\ $\lnot f$}|\makecell{$a, c, \lnot b, $ \\ $\lnot f, \lnot e$}|\makecell{$a, c, \lnot b, $ \\ $\lnot f, \lnot e, d$}}
|
|
\dpllClause{1}{$a, b$}{$a, b$|\done|\done|\done|\done|\done|\done}
|
|
\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done|\done|\done}
|
|
\dpllClause{3}{$c, d$}{$c, d$|$c, d$|\done|\done|\done|\done|\done}
|
|
\dpllClause{4}{$\lnot b, \lnot c$}{$\lnot b, \lnot c$|$\lnot b, \lnot c$|$\lnot b$|\done|\done|\done|\done}
|
|
\dpllClause{5}{$d, e$}{$d, e$|$d, e$|$d, e$|$d, e$|$d, e$|$d$|\done}
|
|
\dpllClause{6}{$\lnot e, f$}{$\lnot e, f$|$\lnot e, f$|$\lnot e, f$|$\lnot e, f$|$\lnot e$|\done|\done}
|
|
\dpllClause{7}{$\lnot d, \lnot f$}{$\lnot d, \lnot f$|$\lnot d, \lnot f$|$\lnot d, \lnot f$|$\lnot d, \lnot f$|\done|\done|\done}
|
|
\dpllClause{8}{$b, \lnot f$}{$b, \lnot f$|$b, \lnot f$|$b, \lnot f$|$\lnot f$|\done|\done|\done}
|
|
\dpllClause{9}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$\lnot b, e$|\done|\done|\done|\done}
|
|
\dpllClause{10}{$a$}{$a$|\done|\done|\done|\done|\done|\done}
|
|
\dpllBCP{$a$|$c$|$\lnot b$|$\lnot f$|$\lnot e$|$d$| - }
|
|
\dpllPL{ - | - | - | - | - | - | - }
|
|
\dpllDeci{ - | - | - | - | - | - |SAT}
|
|
\end{dplltabular}
|
|
}
|
|
|