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Lang:

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Expresión:
x⇒(x⇒y)
(P→Q)∧Q
(P→Q)∧(Q→R)
(P→Q)↔(¬(P∧¬Q))
Expresiones idénticas
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a multiplicar por ¬b multiplicar por c multiplicar por d más ¬a multiplicar por b multiplicar por ¬c multiplicar por d más ¬a multiplicar por b multiplicar por c multiplicar por ¬d más a multiplicar por ¬b multiplicar por ¬c multiplicar por ¬d más ¬a multiplicar por ¬b multiplicar por c multiplicar por ¬d más a multiplicar por ¬b multiplicar por ¬c multiplicar por d más a multiplicar por b multiplicar por ¬c multiplicar por ¬d más a multiplicar por b multiplicar por c multiplicar por d
¬a¬bcd+¬ab¬cd+¬abc¬d+a¬b¬c¬d+¬a¬bc¬d+a¬b¬cd+ab¬c¬d+abcd
Expresiones semejantes
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d-a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d-a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a*¬b*c*d-¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d-a*b*c*d
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d-¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a*¬b*c*d+¬a*b*¬c*d-¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d
¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d-a*b*¬c*¬d+a*b*c*d

Lógica matemática/ ¬a*¬b*c*d+¬a*b*¬c*d+¬a*b*c*¬d+a*¬b*¬c*¬d+¬a*¬b*c*¬d+a*¬b*¬c*d+a*b*¬c*¬d+a*b*c*d

Expresión ¬a¬bcd+¬ab¬cd+¬abc¬d+a¬b¬c¬d+¬a¬bc¬d+a¬b¬cd+ab¬c¬d+abcd

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

Solución

Ha introducido [src]

(a∧b∧c∧d)∨(a∧b∧(¬c)∧(¬d))∨(a∧d∧(¬b)∧(¬c))∨(b∧c∧(¬a)∧(¬d))∨(b∧d∧(¬a)∧(¬c))∨(c∧d∧(¬a)∧(¬b))∨(a∧(¬b)∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b)∧(¬d))

Solución detallada

$$\left(a \wedge b \wedge c \wedge d\right) \vee \left(a \wedge b \wedge \neg c \wedge \neg d\right) \vee \left(a \wedge d \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge \neg b \wedge \neg c \wedge \neg d\right) \vee \left(b \wedge c \wedge \neg a \wedge \neg d\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right) \vee \left(c \wedge d \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg b \wedge \neg d\right) = \left(a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge d\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right)$$

Simplificación [src]

$$\left(a \wedge \neg b \wedge \neg c\right) \vee \left(a \wedge \neg c \wedge \neg d\right) \vee \left(c \wedge \neg a \wedge \neg b\right) \vee \left(c \wedge \neg a \wedge \neg d\right) \vee \left(a \wedge b \wedge c \wedge d\right) \vee \left(b \wedge d \wedge \neg a \wedge \neg c\right)$$

(a∧b∧c∧d)∨(a∧(¬b)∧(¬c))∨(a∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b))∨(c∧(¬a)∧(¬d))∨(b∧d∧(¬a)∧(¬c))

Tabla de verdad

+---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+

FNCD [src]

$$\left(a \vee b \vee c\right) \wedge \left(a \vee c \vee d\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(d \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg d\right)$$

(a∨b∨c)∧(a∨c∨d)∧(b∨(¬a)∨(¬c))∧(d∨(¬a)∨(¬c))∧(a∨(¬b)∨(¬c)∨(¬d))∧(c∨(¬a)∨(¬b)∨(¬d))

FNDP [src]

(a∧b∧c∧d)∨(a∧(¬b)∧(¬c))∨(a∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b))∨(c∧(¬a)∧(¬d))∨(b∧d∧(¬a)∧(¬c))

FND [src]

Ya está reducido a FND

(a∧b∧c∧d)∨(a∧(¬b)∧(¬c))∨(a∧(¬c)∧(¬d))∨(c∧(¬a)∧(¬b))∨(c∧(¬a)∧(¬d))∨(b∧d∧(¬a)∧(¬c))

FNC [src]

$$\left(a \vee \neg a\right) \wedge \left(c \vee \neg c\right) \wedge \left(a \vee b \vee c\right) \wedge \left(a \vee b \vee \neg a\right) \wedge \left(a \vee c \vee d\right) \wedge \left(a \vee c \vee \neg a\right) \wedge \left(a \vee c \vee \neg c\right) \wedge \left(a \vee d \vee \neg a\right) \wedge \left(a \vee \neg a \vee \neg b\right) \wedge \left(a \vee \neg a \vee \neg c\right) \wedge \left(a \vee \neg a \vee \neg d\right) \wedge \left(b \vee c \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg d\right) \wedge \left(c \vee d \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg c \vee \neg d\right) \wedge \left(d \vee \neg a \vee \neg c\right) \wedge \left(d \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee c \vee d\right) \wedge \left(a \vee b \vee c \vee \neg a\right) \wedge \left(a \vee b \vee c \vee \neg b\right) \wedge \left(a \vee b \vee c \vee \neg c\right) \wedge \left(a \vee b \vee c \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg a\right) \wedge \left(a \vee b \vee \neg a \vee \neg b\right) \wedge \left(a \vee b \vee \neg a \vee \neg c\right) \wedge \left(a \vee b \vee \neg a \vee \neg d\right) \wedge \left(a \vee b \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg a\right) \wedge \left(a \vee c \vee d \vee \neg b\right) \wedge \left(a \vee c \vee d \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg d\right) \wedge \left(a \vee c \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee \neg a \vee \neg d\right) \wedge \left(a \vee c \vee \neg b \vee \neg c\right) \wedge \left(a \vee c \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee d \vee \neg a \vee \neg d\right) \wedge \left(a \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg c\right) \wedge \left(b \vee c \vee \neg a \vee \neg c\right) \wedge \left(b \vee c \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee \neg b \vee \neg d\right) \wedge \left(b \vee c \vee \neg c \vee \neg d\right) \wedge \left(b \vee d \vee \neg a \vee \neg c\right) \wedge \left(b \vee d \vee \neg b \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(b \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee \neg a \vee \neg c\right) \wedge \left(c \vee d \vee \neg b \vee \neg c\right) \wedge \left(c \vee d \vee \neg b \vee \neg d\right) \wedge \left(c \vee d \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee c \vee d \vee \neg a\right) \wedge \left(a \vee b \vee c \vee d \vee \neg b\right) \wedge \left(a \vee b \vee c \vee d \vee \neg c\right) \wedge \left(a \vee b \vee c \vee d \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg b\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg c\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg b \vee \neg c\right) \wedge \left(a \vee b \vee c \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee b \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee c \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg a \vee \neg c\right) \wedge \left(b \vee c \vee d \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee d \vee \neg b \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(b \vee c \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(b \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(b \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(b \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(c \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(c \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(d \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee c \vee d \vee \neg a \vee \neg b\right) \wedge \left(a \vee b \vee c \vee d \vee \neg a \vee \neg c\right) \wedge \left(a \vee b \vee c \vee d \vee \neg a \vee \neg d\right) \wedge \left(a \vee b \vee c \vee d \vee \neg b \vee \neg c\right) \wedge \left(a \vee b \vee c \vee d \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee c \vee d \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee c \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee b \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee c \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(a \vee d \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(b \vee c \vee d \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee d \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee c \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(b \vee d \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee d \vee \neg a \vee \neg b \vee \neg c \vee \neg d\right)$$

(a∨(¬a))∧(c∨(¬c))∧(a∨b∨c)∧(a∨c∨d)∧(a∨b∨(¬a))∧(a∨c∨(¬a))∧(a∨c∨(¬c))∧(a∨d∨(¬a))∧(b∨c∨(¬c))∧(c∨d∨(¬c))∧(a∨b∨c∨d)∧(a∨(¬a)∨(¬b))∧(a∨(¬a)∨(¬c))∧(a∨(¬a)∨(¬d))∧(b∨(¬a)∨(¬c))∧(b∨(¬b)∨(¬d))∧(c∨(¬a)∨(¬c))∧(c∨(¬b)∨(¬c))∧(c∨(¬c)∨(¬d))∧(d∨(¬a)∨(¬c))∧(d∨(¬b)∨(¬d))∧(a∨b∨c∨(¬a))∧(a∨b∨c∨(¬b))∧(a∨b∨c∨(¬c))∧(a∨b∨c∨(¬d))∧(a∨b∨d∨(¬a))∧(a∨c∨d∨(¬a))∧(a∨c∨d∨(¬b))∧(a∨c∨d∨(¬c))∧(a∨c∨d∨(¬d))∧(b∨c∨d∨(¬c))∧(a∨b∨(¬a)∨(¬b))∧(a∨b∨(¬a)∨(¬c))∧(a∨b∨(¬a)∨(¬d))∧(a∨b∨(¬b)∨(¬d))∧(a∨c∨(¬a)∨(¬b))∧(a∨c∨(¬a)∨(¬c))∧(a∨c∨(¬a)∨(¬d))∧(a∨c∨(¬b)∨(¬c))∧(a∨c∨(¬c)∨(¬d))∧(a∨d∨(¬a)∨(¬b))∧(a∨d∨(¬a)∨(¬c))∧(a∨d∨(¬a)∨(¬d))∧(a∨d∨(¬b)∨(¬d))∧(b∨c∨(¬a)∨(¬c))∧(b∨c∨(¬b)∨(¬c))∧(b∨c∨(¬b)∨(¬d))∧(b∨c∨(¬c)∨(¬d))∧(b∨d∨(¬a)∨(¬c))∧(b∨d∨(¬b)∨(¬d))∧(c∨d∨(¬a)∨(¬c))∧(c∨d∨(¬b)∨(¬c))∧(c∨d∨(¬b)∨(¬d))∧(c∨d∨(¬c)∨(¬d))∧(a∨b∨c∨d∨(¬a))∧(a∨b∨c∨d∨(¬b))∧(a∨b∨c∨d∨(¬c))∧(a∨b∨c∨d∨(¬d))∧(a∨(¬a)∨(¬b)∨(¬c))∧(a∨(¬a)∨(¬b)∨(¬d))∧(a∨(¬a)∨(¬c)∨(¬d))∧(a∨(¬b)∨(¬c)∨(¬d))∧(b∨(¬a)∨(¬b)∨(¬c))∧(b∨(¬a)∨(¬b)∨(¬d))∧(b∨(¬a)∨(¬c)∨(¬d))∧(b∨(¬b)∨(¬c)∨(¬d))∧(c∨(¬a)∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b)∨(¬d))∧(c∨(¬a)∨(¬c)∨(¬d))∧(c∨(¬b)∨(¬c)∨(¬d))∧(d∨(¬a)∨(¬b)∨(¬c))∧(d∨(¬a)∨(¬b)∨(¬d))∧(d∨(¬a)∨(¬c)∨(¬d))∧(d∨(¬b)∨(¬c)∨(¬d))∧(a∨b∨c∨(¬a)∨(¬b))∧(a∨b∨c∨(¬a)∨(¬c))∧(a∨b∨c∨(¬a)∨(¬d))∧(a∨b∨c∨(¬b)∨(¬c))∧(a∨b∨c∨(¬b)∨(¬d))∧(a∨b∨c∨(¬c)∨(¬d))∧(a∨b∨d∨(¬a)∨(¬b))∧(a∨b∨d∨(¬a)∨(¬c))∧(a∨b∨d∨(¬a)∨(¬d))∧(a∨b∨d∨(¬b)∨(¬d))∧(a∨c∨d∨(¬a)∨(¬b))∧(a∨c∨d∨(¬a)∨(¬c))∧(a∨c∨d∨(¬a)∨(¬d))∧(a∨c∨d∨(¬b)∨(¬c))∧(a∨c∨d∨(¬b)∨(¬d))∧(a∨c∨d∨(¬c)∨(¬d))∧(b∨c∨d∨(¬a)∨(¬c))∧(b∨c∨d∨(¬b)∨(¬c))∧(b∨c∨d∨(¬b)∨(¬d))∧(b∨c∨d∨(¬c)∨(¬d))∧(a∨b∨(¬a)∨(¬b)∨(¬c))∧(a∨b∨(¬a)∨(¬b)∨(¬d))∧(a∨b∨(¬a)∨(¬c)∨(¬d))∧(a∨b∨(¬b)∨(¬c)∨(¬d))∧(a∨c∨(¬a)∨(¬b)∨(¬c))∧(a∨c∨(¬a)∨(¬b)∨(¬d))∧(a∨c∨(¬a)∨(¬c)∨(¬d))∧(a∨c∨(¬b)∨(¬c)∨(¬d))∧(a∨d∨(¬a)∨(¬b)∨(¬c))∧(a∨d∨(¬a)∨(¬b)∨(¬d))∧(a∨d∨(¬a)∨(¬c)∨(¬d))∧(a∨d∨(¬b)∨(¬c)∨(¬d))∧(b∨c∨(¬a)∨(¬b)∨(¬c))∧(b∨c∨(¬a)∨(¬b)∨(¬d))∧(b∨c∨(¬a)∨(¬c)∨(¬d))∧(b∨c∨(¬b)∨(¬c)∨(¬d))∧(b∨d∨(¬a)∨(¬b)∨(¬c))∧(b∨d∨(¬a)∨(¬b)∨(¬d))∧(b∨d∨(¬a)∨(¬c)∨(¬d))∧(b∨d∨(¬b)∨(¬c)∨(¬d))∧(c∨d∨(¬a)∨(¬b)∨(¬c))∧(c∨d∨(¬a)∨(¬b)∨(¬d))∧(c∨d∨(¬a)∨(¬c)∨(¬d))∧(c∨d∨(¬b)∨(¬c)∨(¬d))∧(a∨b∨c∨d∨(¬a)∨(¬b))∧(a∨b∨c∨d∨(¬a)∨(¬c))∧(a∨b∨c∨d∨(¬a)∨(¬d))∧(a∨b∨c∨d∨(¬b)∨(¬c))∧(a∨b∨c∨d∨(¬b)∨(¬d))∧(a∨b∨c∨d∨(¬c)∨(¬d))∧(a∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(b∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(c∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(d∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(a∨b∨c∨(¬a)∨(¬b)∨(¬c))∧(a∨b∨c∨(¬a)∨(¬b)∨(¬d))∧(a∨b∨c∨(¬a)∨(¬c)∨(¬d))∧(a∨b∨c∨(¬b)∨(¬c)∨(¬d))∧(a∨b∨d∨(¬a)∨(¬b)∨(¬c))∧(a∨b∨d∨(¬a)∨(¬b)∨(¬d))∧(a∨b∨d∨(¬a)∨(¬c)∨(¬d))∧(a∨b∨d∨(¬b)∨(¬c)∨(¬d))∧(a∨c∨d∨(¬a)∨(¬b)∨(¬c))∧(a∨c∨d∨(¬a)∨(¬b)∨(¬d))∧(a∨c∨d∨(¬a)∨(¬c)∨(¬d))∧(a∨c∨d∨(¬b)∨(¬c)∨(¬d))∧(b∨c∨d∨(¬a)∨(¬b)∨(¬c))∧(b∨c∨d∨(¬a)∨(¬b)∨(¬d))∧(b∨c∨d∨(¬a)∨(¬c)∨(¬d))∧(b∨c∨d∨(¬b)∨(¬c)∨(¬d))∧(a∨b∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(a∨c∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(a∨d∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(b∨c∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(b∨d∨(¬a)∨(¬b)∨(¬c)∨(¬d))∧(c∨d∨(¬a)∨(¬b)∨(¬c)∨(¬d))

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