1. 1. (H . S) > [ H > (C > W)]
3. H ACP
S MP 3, 2
H . S CN 3,4
6. H > ( C > W) MP 1,5
7. C > W MP 3, 6
8. H > (C > W) CP 3-7

2. C > (A . D)
B > (A . E) / (C v B) > A
3. C v B ACP
4. [C > (A . D)] . [B > (A . E)] CN 1,2
5. (A . D) v (A . E) CD 3,4
6. A . (D v E) DIST 5
7. A SM 6
8. (C v B) > A CP 3-7

3. C > (D v ~E)
E > (D > F) / C > (E > F)
3. C ACP
4. E ACP
5. D v ~E MP 1,3
6. D > F MP 2,4
~ D > ~E IMP 5
E > D TRAN 7
E > F HS 8,6
10. F MP 4, 9
11. E > F CP 4-10
12. C > (E > F) CP 3-11

4. Indirect Proof
Reductio ad absurdem
Assume the conclusion is false, and show that that assumption leads
to a necessarily false statement -- a self-contradiction. This proves that
the assumption is false, which means the originally proposed
conclusion is true.
1. (S v T) > ~S / ~S
2. ~ ~S AIP
3. ~ (S v T) MT 1,2
4. ~S . ~T DM 3
5. ~ S SM 4
6. S . ~S DN, CN 2,5
7. ~S IP 2-6

5. S > (T v ~U)
U > (~T v R)
(S .U) > ~R /~S v ~U
4. ~( ~S v ~U) AIP
5. S . U DM 4
6. S SM 5
7. U CM, SM 5
8. ~R MP 5, 3
9. ~T v R MP 2, 7
10. ~T CM, DS 8, 9
11. T v ~U MP 1,6
12. ~U DS 10,11
13. U . ~U CN 7, 12
14. ~S v ~U IP 4-13