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34 lines
1.2 KiB
34 lines
1.2 KiB
\item \lect Consider the following conflict graph with the following set of clauses:
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\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,
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thick,base node/.style={circle,draw,minimum size=20pt}, real node/.style={double,circle,draw,minimum size=20pt}]
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\node[base node] (1) {$a$};
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\node[base node] (2) [below of=1]{$\lnot b$};
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\node[base node] (3) [right of=1] {$\lnot c$};
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\node[base node] (4) [right of=2] {$d$};
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\node[base node] (5) [right of=3] {$\lnot e$};
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\node[base node] (6) [right of=4] {$e$};
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\node[base node] (7) [right of=5] {$\bot$};
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\path[]
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(1) edge [] node {$1$} (3)
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(2) edge [] node {$3$} (4)
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(4) edge [] node {$1$} (3)
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(3) edge [] node {$6$} (5)
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edge [] node {$7$} (6)
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(5) edge [] node {} (7)
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(6) edge [] node {} (7);
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\end{tikzpicture}
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\begin{dpllCNFInput}
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\item $\{\lnot a, \lnot c, \lnot d\}$
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\item $\{a, \lnot d\}$
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\item $\{b, d\}$
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\item $\{\lnot b, d, e\}$
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\item $\{\lnot b, \lnot e\}$
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\item $\{c, \lnot e\}$
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\item $\{c, e\}$
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\end{dpllCNFInput}
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Give the resolution proof for the given conflict graph and clauses and state the clause to be learned from the conflict.
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