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104 lines
3.2 KiB
104 lines
3.2 KiB
\begin{conflictgraph}
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\node[base node] (notA) {$\lnot a$};
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\node[base node] (B) [right of=notA] {$b$};
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\node[base node] (C) [right of=B] {$c$};
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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 {$7$} (B)
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(B) edge [] node {$3$} (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{$3. \; \lnot b \lor c$}
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\BinaryInfC{$\lnot b$}
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\AxiomC{$7. \; a \lor b$}
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\BinaryInfC{$a$}
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\end{prooftree}
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\begin{dplltabular}{9}
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\dpllStep{(1)|11|12|13|14|15}
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\dpllDecL{0 |0 |0 |0 |0 |0}
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\dpllAssi{-|
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$a$|
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$a, b$|
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$a, b, c$|
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$a, b, c, d$|
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$a, b, c, d, \lnot e$}
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\dpllClause{1}{$a,b,c$}
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{$a,b,c$|\done|\done|\done|\done|\done}
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\dpllClause{2}{$\lnot a,b$}
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{$\lnot a, b$|$b$|\done|\done|\done|\done}
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\dpllClause{3}{$\lnot b, c$}
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{$\lnot b, c$|$\lnot b,c$|$c$|\done|\done|\done}
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\dpllClause{4}{$\lnot c,d$}
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{$\lnot c,d$|$\lnot c,d$|$\lnot c,d$|$d$|\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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{$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot d, \lnot e$|$\lnot e$|$\lnot e$|\done}
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\dpllClause{7}{$a, b$}
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{$a,b$|\done|\done|\done|\done|\done}
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\dpllClause{8}{$a$}
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{$a$|\done|\done|\done|\done|\done}
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\dpllBCP {$a$|$b$|$c$|$d$|$\lnot e$|-}
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\dpllPL {-|-|-|-|-|-}
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\dpllDeci{-|-|-|-|-|UNSAT}
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\end{dplltabular}
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\begin{conflictgraph}
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\node (0){};
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\node[base node] (A) [right of=0] {$a$};
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\node[base node] (B) [right of=A] {$b$};
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\node[base node] (C) [right of=B] {$c$};
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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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(0) edge [] node {8} (A)
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(A) edge [] node {2} (B)
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(B) edge [] node {3} (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{$3. \; \lnot b \lor c$}
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\BinaryInfC{$\lnot b$}
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\AxiomC{$2. \; \lnot a \lor b$}
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\BinaryInfC{$\lnot a$}
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\AxiomC{$8. \; a$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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