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1. (O > R) > S
2. (P > R) > ~S // ~R
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3. (~O v R) > S 1 MI
4. ~(~O v R) v S 3 MI
5. (~~O & ~R) v S 4 DM
6. (O & ~R) v S 5 DN
7. S v (O & ~R) 6 Comm
8. (S v O) & (S v ~R) 7 Dist
9. (S v ~R) & (S v O) 8 Comm
10. S v ~R 9 Simp
11. ~R v S 10 Comm
12. R > S 11 MI
13. ~S > ~R 12 Trans
14. (~P v R) > ~S 2 MI
15. ~(~P v R) v ~S 14 MI
16. (~~P & ~R) v ~S 15 DM
17. (P & ~R) v ~S 16 DN
18. ~S v (P & ~R) 17 Comm
19. (~S v P) & (~S v ~R) 18 Dist
20. (~S v ~R) & (~S v P) 19 Comm
21. ~S v ~R 20 Simp
22. ~R v ~S 21 Comm
23. R > ~S 22 MI
24. R > ~R 23,13 HS
25. ~R v ~R 24 MI
26. ~R 25 Taut
Notes: The abbreviations used are...
MI: Material Implication
DM: De Morgan's Law
DN: Double Negation
Dist: Distribution
Comm: Commutation
Simp: Simplification
Trans: Transposition
HS: Hypothetical Syllogism
Taut: Tautology
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