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100 lines
2.8 KiB
100 lines
2.8 KiB
\begin{dplltabular}{6}
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\dpllStep{1|2|3|4|5|6}
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\dpllDecL{0|1|2|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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$\lnot a, \lnot b, c, d$|
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$\lnot a, \lnot b, c, d, e$}
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\dpllClause{1}{$a,b,c$}
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{$a,b,c$|$b,c$|$c$|\done|\done|\done}
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\dpllClause{2}{$\lnot a,b$}
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{$\lnot a,b$|\done|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot b, c$}
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{$\lnot b, c$|$\lnot b, c$|\done|\done|\done|\done}
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\dpllClause{4}{$\lnot c,d$}
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{$\lnot c,d$|$\lnot c,d$|$\lnot c,d$|$d$|\done|\done}
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\dpllClause{5}{$\lnot c,e$}
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{$\lnot c,e$|$\lnot c,e$|$\lnot c,e$|$e$|$e$|\conflict}
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\dpllClause{6}{$\lnot d, \lnot e$}
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{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
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\dpllBCP {-|-|$c$|$d$|$\lnot e$|-}
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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] (D) [below right of=C] {$d$};
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\node[base node] (E) [right of=C] {$e$};
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\node[base node] (notE) [right of=D] {$\lnot e$};
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\node[base node] (bot) [above right of=notE] {$\bot$};
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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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(C) edge [] node {$4$} (D)
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(C) edge [] node {$5$} (E)
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(D) edge [] node {$6$} (notE)
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(notE) edge [] node {} (bot)
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(E) edge [] node {} (bot);
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\end{conflictgraph}
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\begin{prooftree}
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\AxiomC{$6. \; \lnot d \lor \lnot e$}
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\AxiomC{$4. \; \lnot c \lor d$}
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\BinaryInfC{$\lnot e \lor \lnot c$}
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\AxiomC{$5. \; \lnot c \lor e$}
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\BinaryInfC{$\lnot c$}
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\AxiomC{$1. \; a \lor b \lor c$}
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\BinaryInfC{$a \lor b$}
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\end{prooftree}
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\begin{dplltabular}{9}
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\dpllStep{(2)|7|8|9|10}
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\dpllDecL{1 |1|1|1|1}
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\dpllAssi{$\lnot a$|
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$\lnot a, b$|
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$\lnot a, b, c$|
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$\lnot a, b, c, d$|
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$\lnot a, b, c, d, \lnot e$}
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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}{$\lnot a,b$}
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{\done|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot b, c$}
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{$\lnot b, c$|$c$|\done|\done|\done}
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\dpllClause{4}{$\lnot c,d$}
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{$\lnot c,d$|$\lnot c,d$|$d$|\done|\done}
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\dpllClause{5}{$\lnot c,e$}
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{$\lnot c,e$|$\lnot c,e$|$e$|$e$|\conflict}
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\dpllClause{6}{$\lnot d, \lnot e$}
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{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|\done}
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\dpllClause{7}{$a, b$}
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{$b$|\done|\done|\done|\done}
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\dpllBCP {$b$|$c$|$d$|$\lnot e$|-}
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\dpllPL {-|-|-|-|-}
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\dpllDeci{-|-|-|-|-}
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\end{dplltabular}
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