1. A very difficult problem There is nothing to do, so try -Out.
Strategy Review
A very difficult problem
1. -(A>B) A
A GOAL
There is nothing to do, so try -Out.

2. Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA ?&-?
A ? -O
-(A>B) is available so use it as part of the contradiction.

3. Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA
(A>B)&-(A>B) 1,? &I
A ? -O
To get this contradiction we will need to prove A>B.

4. Strategy Review A very difficult problem 1. -(A>B) A 2. -A PA
A>B GOAL
(A>B)&-(A>B) 1,? &I
A ? -O
Since the GOAL is a conditional,
use the >In strategy

5. A very difficult problem We are stuck. So use the Negation Strategy
Strategy Review
A very difficult problem
1. -(A>B) A
A PA
A PA
B GOAL
A>B 3-? >I
(A>B)&-(A>B) 1,? &I
A ? -O
We are stuck. So use the Negation Strategy

6. A very difficult problem What is our contradiction?
Strategy Review
A very difficult problem
1. -(A>B) A
A PA
A PA
B PA
?&-?
B 4-? -O
A>B 3-? >I
(A>B)&-(A>B) 1,? &I
A ? -O
What is our contradiction?

7. A very difficult problem
Strategy Review
A very difficult problem
1. -(A>B) A
A PA
A PA
B PA
A&-A 3,2 &I
B 4-5 -O
A>B 3-6 >I
8. (A>B)&-(A>B) 1,7 &I
9. A O
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