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112 lines
4.3 KiB
112 lines
4.3 KiB
\hspace{-0.09cm}\scalebox{0.85}{
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\begin{dplltabular}{5}
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\dpllStep{1|2|3|4|5}
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\dpllDecL{0|1|1|1|1}
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\dpllAssi{ - |$\lnot a$|$\lnot a, \lnot b$|$\lnot a, \lnot b, \lnot c$|\makecell{$\lnot a, \lnot b, \lnot c, $ \\ $\lnot d$}}
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\dpllClause{1}{$b, \lnot d, a$}{$b, \lnot d, a$|$b, \lnot d$|$\lnot d$|$\lnot d$|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot a, b, c$}{$\lnot a, b, c$|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|\done|\done|\done}
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\dpllClause{5}{$a, d$}{$a, d$|$d$|$d$|$d$|\conflict}
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\dpllClause{6}{$a, \lnot c$}{$a, \lnot c$|$\lnot c$|$\lnot c$|\done|\done}
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\dpllClause{7}{$\lnot a, \lnot e, \lnot d$}{$\lnot a, \lnot e, \lnot d$|\done|\done|\done|\done}
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\dpllClause{8}{$a, \lnot b$}{$a, \lnot b$|$\lnot b$|\done|\done|\done}
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\dpllBCP{ - |$\lnot b$|$\lnot c$|$\lnot d$| - }
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\dpllPL{ - | - | - | - | - }
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\dpllDeci{$\lnot a$| - | - | - | - }
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\end{dplltabular}
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}
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Conflict in step 5\\
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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 {$$5$$};
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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 {$$8$$};
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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 {$\lnot a$};
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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 {$\lnot d$};
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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 {$d$};
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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 {$\lnot b$};
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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{$1. \; b \lor \lnot d \lor a$}
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\AxiomC{$5. \; a \lor d$}
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\BinaryInfC{$b \lor a$}
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\AxiomC{$8. \; a \lor \lnot b$}
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\BinaryInfC{$a$}
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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{6|7|8|9|10}
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\dpllDecL{0|0|0|0|0}
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\dpllAssi{ - |$a$|$a, c$|$a, c, \lnot b$|\makecell{$a, c, \lnot b, $ \\ $\lnot d$}}
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\dpllClause{1}{$b, \lnot d, a$}{$b, \lnot d, a$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot a, c$}{$\lnot a, c$|$c$|\done|\done|\done}
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\dpllClause{3}{$\lnot a, b, c$}{$\lnot a, b, c$|$b, c$|\done|\done|\done}
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\dpllClause{4}{$\lnot b, e$}{$\lnot b, e$|$\lnot b, e$|$\lnot b, e$|\done|\done}
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\dpllClause{5}{$a, d$}{$a, d$|\done|\done|\done|\done}
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\dpllClause{6}{$a, \lnot c$}{$a, \lnot c$|\done|\done|\done|\done}
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\dpllClause{7}{$\lnot a, \lnot e, \lnot d$}{$\lnot a, \lnot e, \lnot d$|$\lnot e, \lnot d$|$\lnot e, \lnot d$|$\lnot e, \lnot d$|\done}
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\dpllClause{8}{$a, \lnot b$}{$a, \lnot b$|\done|\done|\done|\done}
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\dpllClause{9}{$a$}{$a$|\done|\done|\done|\done}
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\dpllBCP{$a$|$c$| - | - | - }
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\dpllPL{ - | - |$\lnot b$|$\lnot d$| - }
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\dpllDeci{ - | - | - | - |SAT}
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\end{dplltabular}
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}
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