1. (G • S) → D
2. (S → D) → P
3. G /P
| 4. ~P Assumption for indirect proof
| 5. ~(S → D) 2,4, Modus tollens
| 6. ~(~S v D) 5, Material implication
| 7. ~~S • ~D 6, deMorgan's law
| 8. S • ~D 7, double negation
| 9. ~D • S 8, commutation
|10. ~D 9, simplification
|11. ~(G • S) 1,10, Modus tollens
|12. ~G v ~S 11, deMorgan's law
|13. S • ~D 9, commutation
|14. S 13, simplification
|15. ~S v ~G 12, commutation
|16. ~~S 14, double negation
|17. ~G 15,16 disjunctive syllogism
|18. G • ~G 2,17 conjunction
19. P Lines 4-18 for indirect proof
Edwin