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