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108 lines
4.0 KiB
108 lines
4.0 KiB
\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{4}
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\dpllStep{1|2|3|4}
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\dpllDecL{0|1|1|1}
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\dpllAssi{ - |$\lnot w$|$\lnot w, \lnot x$|$\lnot w, \lnot x, \lnot y$}
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\dpllClause{1}{$x, y, w$}{$x, y, w$|$x, y$|$y$|\conflict}
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\dpllClause{2}{$\lnot x, z, \lnot w$}{$\lnot x, z, \lnot w$|\done|\done|\done}
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\dpllClause{3}{$\lnot y, w$}{$\lnot y, w$|$\lnot y$|$\lnot y$|\done}
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\dpllClause{4}{$\lnot z, \lnot w$}{$\lnot z, \lnot w$|\done|\done|\done}
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\dpllClause{5}{$\lnot y, z$}{$\lnot y, z$|$\lnot y, z$|$\lnot y, z$|\done}
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\dpllClause{6}{$\lnot x, w$}{$\lnot x, w$|$\lnot x$|\done|\done}
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\dpllBCP{ - |$\lnot x$|$\lnot y$| - }
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\dpllPL{ - | - | - | - }
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\dpllDeci{$\lnot w$| - | - | - }
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\end{dplltabular}
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}
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Conflict in step 4\\
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\scalebox{0.75}{
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\begin{tikzpicture}[>=latex,line join=bevel,]
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\pgfsetlinewidth{1bp}
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%%
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\pgfsetcolor{black}
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% Edge: 1 -> 3
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\draw [->] (22.223bp,55.0bp) .. controls (50.414bp,55.0bp) and (129.66bp,55.0bp) .. (177.75bp,55.0bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (100.0bp,62.5bp) node {$$1$$};
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% Edge: 1 -> 4
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\draw [->] (18.027bp,46.114bp) .. controls (23.074bp,39.428bp) and (30.901bp,30.65bp) .. (40.0bp,26.0bp) .. controls (66.949bp,12.229bp) and (102.57bp,9.9572bp) .. (134.8bp,10.34bp);
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\draw (54.0bp,33.5bp) node {$$3$$};
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% Edge: 1 -> 5
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\draw [->] (21.311bp,59.709bp) .. controls (35.439bp,66.854bp) and (62.567bp,80.574bp) .. (89.756bp,94.325bp);
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\draw (54.0bp,90.5bp) node {$$6$$};
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% Edge: 3 -> 2
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\draw [->] (199.16bp,50.341bp) .. controls (207.09bp,46.306bp) and (218.8bp,40.346bp) .. (237.68bp,30.744bp);
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% Edge: 4 -> 2
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\draw [->] (156.95bp,12.493bp) .. controls (173.2bp,14.93bp) and (205.73bp,19.81bp) .. (237.09bp,24.513bp);
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% Edge: 5 -> 3
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\draw [->] (110.31bp,94.291bp) .. controls (124.44bp,87.146bp) and (151.57bp,73.426bp) .. (178.76bp,59.675bp);
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\draw (146.0bp,90.5bp) node {$$1$$};
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% Node: 1
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (11.0bp,55.0bp) ellipse (11.0bp and 11.0bp);
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\draw (11.0bp,55.0bp) node {$\lnot w$};
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\end{scope}
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% Node: 3
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (189.0bp,55.0bp) ellipse (11.0bp and 11.0bp);
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\draw (189.0bp,55.0bp) node {$y$};
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\end{scope}
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% Node: 4
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (146.0bp,11.0bp) ellipse (11.0bp and 11.0bp);
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\draw (146.0bp,11.0bp) node {$\lnot y$};
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\end{scope}
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% Node: 5
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (100.0bp,99.0bp) ellipse (11.0bp and 11.0bp);
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\draw (100.0bp,99.0bp) node {$\lnot x$};
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\end{scope}
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% Node: 2
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (248.0bp,26.0bp) ellipse (11.0bp and 11.0bp);
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\draw (248.0bp,26.0bp) node {$\bot$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\begin{prooftree}
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\AxiomC{$1. \; x \lor y \lor w$}
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\AxiomC{$3. \; \lnot y \lor w$}
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\BinaryInfC{$x \lor w$}
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\AxiomC{$6. \; \lnot x \lor w$}
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\BinaryInfC{$w$}
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\end{prooftree}
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\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{5}
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\dpllStep{5|6|7|8|9}
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\dpllDecL{0|0|0|0|0}
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\dpllAssi{ - |$w$|$w, \lnot z$|$w, \lnot z, \lnot x$|\makecell{$w, \lnot z, \lnot x, $ \\ $\lnot y$}}
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\dpllClause{1}{$x, y, w$}{$x, y, w$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot x, z, \lnot w$}{$\lnot x, z, \lnot w$|$\lnot x, z$|$\lnot x$|\done|\done}
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\dpllClause{3}{$\lnot y, w$}{$\lnot y, w$|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot z, \lnot w$}{$\lnot z, \lnot w$|$\lnot z$|\done|\done|\done}
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\dpllClause{5}{$\lnot y, z$}{$\lnot y, z$|$\lnot y, z$|$\lnot y$|$\lnot y$|\done}
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\dpllClause{6}{$\lnot x, w$}{$\lnot x, w$|\done|\done|\done|\done}
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\dpllClause{7}{$w$}{$w$|\done|\done|\done|\done}
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\dpllBCP{$w$|$\lnot z$|$\lnot x$|$\lnot y$| - }
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\dpllPL{ - | - | - | - | - }
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\dpllDeci{ - | - | - | - |SAT}
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\end{dplltabular}
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}
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