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put this solution on YOUR website! The idea with these derivations is to include all of the given premises. It helps to fully know the 19 rules of inference (preferably by heart) so you might be able to recognize the answer easier.
Here is one way to do it...
1. (G * P) -> K
2. E -> Z
3. ~P -> ~Z
4. G ->(E v L) :. (G * ~L) -> K
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5. ~~Z -> ~~P 3 Transposition
6. Z -> P 5 Double Negation
7. E -> P 2,6 Hypothetical Syllogism
8. (P * G) -> K 1 Commutation
9. P -> (G -> K) 8 Exportation
10. E -> (G -> K) 7,9 Hypothetical Syllogism
11. ~G v (E v L) 4 Material Implication
12. (~G v E) v L 11 Association
13. (E v ~G) v L 12 Commutation
14. (~~E v ~G) v L 13 Double Negation
15. ~(~E * G) v L 14 De Morgan's Law
16. (~E * G) -> L 15 Material Implication
17. ~E -> (G -> L) 16 Exportation
18. ~(G -> L) -> ~~E 17 Transposition
19. ~(G -> L) -> E 18 Double Negation
20. ~(G -> L) -> (G -> K) 19,10 Hypothetical Syllogism
21. (G -> L) v (G -> K) 20 Material Implication
22. (~G v L) v (~G v K) 21 Material Implication
23. ~G v (L v ~G) v K 22 Association
24. ~G v (~G v L) v K 23 Commutation
25. (~G v ~G) v (L v K) 24 Association
26. ~G v (L v K) 25 Tautology
27. (~G v L) v K 26 Association
28. (~G v ~~L) v K 27 Double Negation
29. ~(G * ~L) v K 28 De Morgan's Law
30. (G * ~L) -> K 29 Material Implication
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