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92 lines
3.0 KiB
92 lines
3.0 KiB
\begin{dplltabular}{5}
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\dpllStep{1|2|3|4|5}
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\dpllDecL{0|1|2|2|2}
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\dpllAssi{-|
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$\lnot a$|
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$\lnot a, \lnot b$|
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$\lnot a, \lnot b, c$|
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$\lnot a, \lnot b, c, \lnot d$}
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\dpllClause{1}{$a,b,c$}
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{$a,b,c$|$b,c$|$c$|\done|\done}
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\dpllClause{2}{$\lnot a, \lnot b, \lnot c$}
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{$\lnot a, \lnot b, \lnot c$|\done|\done|\done|\done}
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\dpllClause{3}{$a,c,\lnot e$}
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{$a,c,\lnot e$|$c,\lnot e$|$c,\lnot e$|\done|\done}
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\dpllClause{4}{$\lnot b, \lnot c, e$}
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{$\lnot b, \lnot c, e$|$\lnot b, \lnot c, e$|\done|\done|\done}
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\dpllClause{5}{$b, e$}
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{$b, e$|$b, e$|$e$|$e$|$e$}
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\dpllClause{6}{$b, \lnot d$}
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{$b, \lnot d$|$b, \lnot d$|$\lnot d$|$\lnot d$|\done}
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\dpllClause{7}{$\lnot c, d$}
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{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\conflict}
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\dpllClause{8}{$\lnot c, e$}
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{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|$e$|$e$}
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\dpllBCP{-|-|$c$|$\lnot d$|-}
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\dpllPL{-|-|-|-|-}
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\dpllDeci{$\lnot a$|$\lnot b$|-|-|-}
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\end{dplltabular}
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\begin{conflictgraph}
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\node[base node] (notA) {$\lnot a$};
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\node[base node] (notB) [below of=notA] {$\lnot b$};
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\node[base node] (C) [right of=notA] {$c$};
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\node[base node] (notD) [right of=notB] {$\lnot d$};
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\node[base node] (D) [right of=C] {$d$};
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\node[base node] (bot) [below right of=D] {$\bot$};
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\path[]
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(notA) edge [] node {1} (C)
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(notB) edge [] node {1} (C)
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(notB) edge [] node {6} (notD)
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(C) edge [] node {7} (D)
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(notD) edge [] node {} (bot)
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(D) edge [] node {} (bot);
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\end{conflictgraph}
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\begin{prooftree}
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\AxiomC{$7. \; \clause{\lnot c;d}$}
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\AxiomC{$6. \; \clause{b;\lnot d}$}
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\BinaryInfC{$\clause{b;\lnot c}$}
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\AxiomC{$1. \; \clause{a;b;c}$}
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\BinaryInfC{$\clause{a;b}$}
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\end{prooftree}
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\begin{dplltabular}{5}
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\dpllStep{(1)|6|7|8|9}
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\dpllDecL{1 |1|1|2|2 }
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\dpllAssi{$\lnot a$|
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$\lnot a, b$|
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$\lnot a, b, d$|
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$\lnot a, b, d, \lnot c$|
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$\lnot a, b, d, \lnot c,\lnot e$}
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\dpllClause{1}{$a,b,c$}
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{$b,c$|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot c, d$}
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{$\lnot c, d$|$\lnot c, d$|\done|\done|\done}
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\dpllClause{3}{$\lnot c, e$}
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{$\lnot c, e$|$\lnot c, e$|$\lnot c, e$|\done|\done}
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\dpllClause{4}{$\lnot a, \lnot b, \lnot c$}
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{\done|\done|\done|\done|\done}
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\dpllClause{5}{$a,c,\lnot e$}
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{$c,\lnot e$|$c,\lnot e$|$c,\lnot e$|$\lnot e$|\done}
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\dpllClause{6}{$\lnot b, \lnot c, e$}
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{$\lnot b, \lnot c, e$|$\lnot c,e$|$\lnot c,e$|\done|\done}
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\dpllClause{7}{$b, e$}
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{$b, e$|\done|\done|\done|\done}
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\dpllClause{8}{$b, \lnot d$}
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{$b, \lnot d$|\done|\done|\done|\done}
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\dpllClause{9}{$a, b$}
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{$b$|\done|\done|\done|\done}
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\dpllBCP {$b$|-|-|$\lnot e$|-}
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\dpllPL {-|$d$|-|-|-}
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\dpllDeci{-|-|$\lnot c$|-|SAT}
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\end{dplltabular}
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