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Beispiel für die Transformation einer Formel in Klauselform

Transformiere die folgende Formel in Klauselform: $$ (\neg( \neg ((a \land b) \lor c) \lor (b \lor c) ) \land \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) ) $$

$$ \langle $$ $$ (\neg( \neg ((a \land b) \lor c) \lor (b \lor c) ) \land \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) ) $$ $$ \rangle $$ (2)
$$ \langle [ $$ $$ \neg( \neg ((a \land b) \lor c) \lor (b \lor c) $$ $$ ] , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (5)
$$ \langle [ $$ $$ \neg\neg ((a \land b) \lor c) $$ $$ ] , [ $$ $$ \neg (b \lor c) $$ $$ ] , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (1)
$$ \langle [ $$ $$ ((a \land b) \lor c) $$ $$ ] , [ $$ $$ \neg (b \lor c) $$ $$ ] , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (4)
$$ \langle [ $$ $$ (a \land b) $$ $$ , $$ $$ c~~ $$ $$ ] , [ $$ $$ \neg (b \lor c) $$ $$ ] , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (2)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , [ $$ $$ \neg (b \lor c) $$ $$ ] , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (5)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , [ $$ $$ \neg( ( a \land b ) \land ( (d \lor c) \lor d) ) $$ $$ ] \rangle $$ (3)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , [ $$ $$ \neg ( a \land b ) $$ $$ , $$ $$ \neg ((d \lor c) \lor d) $$ $$ ] \rangle $$ (3)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , [ $$ $$ \neg a , \neg b $$ $$ , $$ $$ \neg ((d \lor c) \lor d) $$ $$ ] \rangle $$ (5)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , [ $$ $$ \neg a, \neg b , $$ $$ \neg (d \lor c) $$ $$ ] , [ $$ $$ \neg a, \neg b, \neg d $$ $$ ] \rangle $$ (5)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , $$ $$ [ \neg a, \neg b , \neg d ] $$ $$ , $$ $$ [ \neg a, \neg b , \neg c ] $$ $$ , $$ $$ [ \neg a, \neg b , \neg d ] $$ $$ \rangle $$ (Idempotenz)
$$ \langle $$ $$ [~~a , c~~] $$ $$ , $$ $$ [~~b , c~~] $$ $$ , $$ $$ [~~ \neg b~~] $$ $$ , $$ $$ [~~\neg c~~] $$ $$ , $$ $$ [ \neg a, \neg b , \neg d ] $$ $$ , $$ $$ [ \neg a, \neg b , \neg c ] $$ $$ \rangle $$

Beispiel für die Transformation einer Formel in Klauselform. Pro Schritt werden die jeweils betrachteten Teilformeln gelb hinterlegt. Das Umformungsresultat ist grün hinterlegt.