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A Harder Example. (PvQ)>R -[(P>R)&(Q>R)]. (PvQ)>R | (P>R)&(Q>R). A Harder Example. (PvQ)>R -[(P>R)&(Q>R)]. (PvQ)>R | (P>R)&(Q>R). A Harder Example. (-&) Rule -(A&B) -A -B. (PvQ)>R -[(P>R)&(Q>R)]. (PvQ)>R | (P>R)&(Q>R). A Harder Example. 1. (-&) Rule -(A&B)

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A Harder Example

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A harder example

A Harder Example

(PvQ)>R

-[(P>R)&(Q>R)]

(PvQ)>R | (P>R)&(Q>R)


A harder example1

A Harder Example

(PvQ)>R

-[(P>R)&(Q>R)]

(PvQ)>R | (P>R)&(Q>R)


A harder example2

A Harder Example

(-&) Rule

-(A&B)

-A -B

(PvQ)>R

-[(P>R)&(Q>R)]

(PvQ)>R | (P>R)&(Q>R)


A harder example3

A Harder Example

1

(-&) Rule

-(A&B)

-A -B

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)


A harder example4

A Harder Example

1

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)


A harder example5

A Harder Example

1

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

(->) Rule

-(A>B)

A

-B


A harder example6

A Harder Example

1

2

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

(->) Rule

-(A>B)

A

-B

P

-R


A harder example7

A Harder Example

1

2

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

(->) Rule

-(A>B)

A

-B

P

-R


A harder example8

A Harder Example

1

2

3

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

(->) Rule

-(A>B)

A

-B

P

-R

Q

-R


A harder example9

A Harder Example

1

2

3

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R


A harder example10

A Harder Example

1

2

3

(>) Rule

A>B

-A B

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R


A harder example11

A Harder Example

1

2

3

(>) Rule

A>B

-A B

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

THE RESULT OF APPLYINGA RULE MUST APPEAR ONEVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.


A harder example12

A Harder Example

1

2

3

4

(>) Rule

A>B

-A B

-(PvQ) R

-(PvQ) R

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

THE RESULT OF APPLYINGA RULE MUST APPEAR ONEVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.


A harder example13

A Harder Example

1

2

3

4

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R


A harder example14

A Harder Example

1

2

3

4

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R


A harder example15

A Harder Example

1

2

3

4

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

(-v) Rule

-(AvB)

-A

-B


A harder example16

A Harder Example

1

2

3

4

5

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

(-v) Rule

-(AvB)

-A

-B

-P

-Q


A harder example17

A Harder Example

1

2

3

4

5

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

(-v) Rule

-(AvB)

-A

-B

-P

-Q

-(AvB) =

-A&-B


A harder example18

A Harder Example

1

2

3

4

5

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

(-v) Rule

-(AvB)

-A

-B

-P

-Q


A harder example19

A Harder Example

1

2

3

4

5

6

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

(-v) Rule

-(AvB)

-A

-B

-P

-Q

-P

-Q


A harder example20

A Harder Example

1

2

3

4

5

6

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

P

-R

Q

-R

-P

-Q

*

-P

-Q

*


A harder example21

A Harder Example

5

1

2

3

4

6

-(PvQ) R

*

-(PvQ) R

*

(PvQ)>R

-[(P>R)&(Q>R)]

-(P>R) -(Q>R)

(PvQ)>R | (P>R)&(Q>R)

VALID

P

-R

Q

-R

-P

-Q

*

-P

-Q

*


Ordering strategy

Ordering Strategy

It is best to do non-branching steps first.

For more click here


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