1.) (L=N) > C

2.) (L=N) v (P>~E)
3.) ~E > C
4.) ~C /~P

To solve this problem, we can use natural deduction and proof by contradiction. Here's how we can derive the conclusion ~P from the given premises:

1. (L=N) > C [Premise]
2. (L=N) v (P>~E) [Premise]
3. ~E > C [Premise]
4. ~C [Premise]
5. ~P [To be derived]

Assume P. We will show that this leads to a contradiction:

6. L=N v (P>~E) [Lines 2]
7. (L=N) > C [Lines 1]
8. P > ~E [Lines 6, Disjunctive Syllogism]
9. ~E [Lines 8, P]
10. C [Lines 7, 9, Modus Ponens]
11. ~C & C [Lines 4, 10, Conjunction]
12. ~P [Lines 6-11, Proof by Contradiction]

Since assuming P leads to a contradiction, we can conclude ~P.