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.
 
 

118 lines
4.3 KiB

\hspace{-0.09cm}\scalebox{0.85}{
\begin{dplltabular}{6}
\dpllStep{12|13|14|15|16|17}
\dpllDecL{0|0|0|0|0|0}
\dpllAssi{ - |$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $d$}|\makecell{$a, b, c, $ \\ $d, \lnot e$}}
\dpllClause{1}{$a, b, c$}{$a, b, c$|\done|\done|\done|\done|\done}
\dpllClause{2}{$\lnot a, b$}{$\lnot a, b$|$b$|\done|\done|\done|\done}
\dpllClause{3}{$\lnot b, c$}{$\lnot b, c$|$\lnot b, c$|$c$|\done|\done|\done}
\dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done|\done}
\dpllClause{5}{$\lnot c, e$}{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$|\conflict}
\dpllClause{6}{$\lnot d, \lnot e$}{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
\dpllClause{7}{$a, b$}{$a, b$|\done|\done|\done|\done|\done}
\dpllClause{8}{$a$}{$a$|\done|\done|\done|\done|\done}
\dpllBCP{$a$|$b$|$c$|$d$|$\lnot e$| - }
\dpllPL{ - | - | - | - | - | - }
\dpllDeci{ - | - | - | - | - |UNSAT}
\end{dplltabular}
}
Conflict in step 17\\
\scalebox{0.75}{
\begin{tikzpicture}[>=latex,line join=bevel,]
\pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
% Edge: 0 -> 7
\draw [->] (1.0536bp,30.0bp) .. controls (2.5071bp,30.0bp) and (33.188bp,30.0bp) .. (64.696bp,30.0bp);
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (33.0bp,37.5bp) node {$$8$$};
% Edge: 2 -> 3
\draw [->] (173.3bp,30.0bp) .. controls (186.47bp,30.0bp) and (209.58bp,30.0bp) .. (236.88bp,30.0bp);
\draw (205.0bp,37.5bp) node {$$3$$};
% Edge: 3 -> 4
\draw [->] (258.97bp,32.373bp) .. controls (272.23bp,35.53bp) and (295.98bp,41.186bp) .. (323.05bp,47.63bp);
\draw (291.0bp,49.5bp) node {$$4$$};
% Edge: 3 -> 5
\draw [->] (258.07bp,25.196bp) .. controls (263.42bp,22.594bp) and (270.42bp,19.594bp) .. (277.0bp,18.0bp) .. controls (303.72bp,11.525bp) and (335.6bp,10.402bp) .. (366.0bp,10.619bp);
\draw (291.0bp,25.5bp) node {$$5$$};
% Edge: 4 -> 6
\draw [->] (345.3bp,50.0bp) .. controls (358.47bp,50.0bp) and (381.58bp,50.0bp) .. (408.88bp,50.0bp);
\draw (377.0bp,57.5bp) node {$$6$$};
% Edge: 5 -> 1
\draw [->] (387.95bp,12.194bp) .. controls (404.12bp,14.134bp) and (436.4bp,18.008bp) .. (467.79bp,21.775bp);
% Edge: 6 -> 1
\draw [->] (430.16bp,45.662bp) .. controls (438.01bp,41.945bp) and (449.56bp,36.472bp) .. (468.68bp,27.417bp);
% Edge: 7 -> 2
\draw [->] (87.3bp,30.0bp) .. controls (100.47bp,30.0bp) and (123.58bp,30.0bp) .. (150.88bp,30.0bp);
\draw (119.0bp,37.5bp) node {$$2$$};
% Node: 7
\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}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (479.0bp,23.0bp) ellipse (11.0bp and 11.0bp);
\draw (479.0bp,23.0bp) node {$\bot$};
\end{scope}
% Node: 2
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (162.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
\draw (162.0bp,30.0bp) node {$b$};
\end{scope}
% Node: 3
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (248.0bp,30.0bp) ellipse (11.0bp and 11.0bp);
\draw (248.0bp,30.0bp) node {$c$};
\end{scope}
% Node: 4
\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 {$d$};
\end{scope}
% Node: 5
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (377.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
\draw (377.0bp,11.0bp) node {$e$};
\end{scope}
% Node: 6
\begin{scope}
\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
\pgfsetstrokecolor{strokecol}
\draw (420.0bp,50.0bp) ellipse (11.0bp and 11.0bp);
\draw (420.0bp,50.0bp) node {$\lnot e$};
\end{scope}
%
\end{tikzpicture}
}
\begin{prooftree}
\AxiomC{$6. \; \lnot d \lor \lnot e$}
\AxiomC{$4. \; \lnot c \lor d$}
\BinaryInfC{$\lnot e \lor \lnot c$}
\AxiomC{$5. \; \lnot c \lor e$}
\BinaryInfC{$\lnot c$}
\AxiomC{$3. \; \lnot b \lor c$}
\BinaryInfC{$\lnot b$}
\AxiomC{$2. \; \lnot a \lor b$}
\BinaryInfC{$\lnot a$}
\AxiomC{$8. \; a$}
\BinaryInfC{$\bot$}
\end{prooftree}