Since we have the conclusion N, let's assume for the sake of argument that the opposite is true. In other words, let's assume that the conclusion is ~N. Our job is to show that a contradiction will arise, and if it does, then the opposite of ~N must be true (ie N is really the correct conclusion).
1.) (K > K) > R
2.) (R v M) > N / N
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3.) ~N AIP
4.) ~(R v M) 2,3 Modus Tollens
5.) ~R & ~M 4 De Morgan's Law
6.) ~R 5 Simplification
7.) ~(K > K) 1,6 Modus Tollens
8.) ~(~K v K) 7 Material Implication
9.) ~~K & ~K 8 De Morgan's Law
10.) K & ~K 9 Double Negation
11.) N 3-10 IP