Combining > with - Strategies C > -P A[1] 1 P > CGOAL[2] Since the GOAL has the form A > B, use the > In Strategy

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] CGOAL[4] 1 P > C2-? > I[2] Since the GOAL has the form A > B, use the > In Strategy

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] CGOAL[4] 1 P > C2-? > I[2] Since nothing can be done, try the -Out Strategy

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] ?&-? GOAL C3-? -O[4] 1 P > C2-? > I[2] What should the Contradiction be?

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] ?&-? GOAL C3-? -O[4] 1 P > C2-? > I[2] What should the Contradiction be? DON’T CHOOSE C&-C!

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] C ????? C&-C GOAL C3-? -O[4] 1 P > C2-? > I[2] What should the Contradiction be? DON’T CHOOSE C&-C!

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] P&-P GOAL[6] C3-? -O[4] 1 P > C2-? > I[2] Choose “new” material for a contradiction.

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] 4. -P 1,3 > O [7] P&-P GOAL[6] C3-? -O[4] 1 P > C2-? > I[2]

Combining > with - Strategies C > -P A[1] 2 2. P PA[3] C PA[5] 1,34. -P 1,3 > O [7] 1,2,3 5. P&-P 2,4 &I[6] 1,26. C3-5 -O[4] 17. P > C2-6 > I[2]

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 1,2 P > IGOAL[2] See p. 116 of your book. The goal has the form A > B, so use the > In strategy

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] IGOAL[4] 1,2 P > I3-? > I[2] How can we get I?

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] IGOAL[4] 1,2 P > I3-? > I[2] The GOAL I is to the right of an arrow in line 2!

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] AGOAL[5] I2,? > O[4] 1,2 P > I3-? > I[2] The GOAL I is to the right of an arrow in line 2! So set the antecedent A as a new GOAL.

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] AGOAL[5] I2,? > O[4] 1,2 P > I3-? > I[2] How can we get A? Nothing can be done, so use -Out.

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] A PA[6] ?&-? GOAL[7] A4-? -O[5] I2,? > O[4] 1,2 P > I3-? > I[2] What contradiction should we try for?

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] A PA[6] P&-P 3,? &I[7] A4-? -O[5] I2,? > O[4] 1,2 P > I3-? > I[2]

Combining > with - Strategies A > -P A[1] 22. A > IA[2] 3 3. P PA[3] A PA[6] 1,45. -P 1,4 > O [8] 1,3,4 6. P&-P 3,5 &I[7] 1,37. A4-6 -O[5] 1,2,38. I2,7 > O[4] 1,27. P > I3-8 > I[2] For more click here