Act as a Professor of Formal Logic. Construct a step-by-step natural deduction proof for the following argument: Premise 1: If the library is open (L), then the study room is available (S) or the computers are on (C). Premise 2: If the study room is available, then the quiet zone is closed (Q). Premise 3: The library is open (L) and the quiet zone is not closed (~Q). Conclusion: Therefore, the computers are on (C). Explicitly state the rules of inference used (Modus Ponens, Modus Tollens, Disjunctive Syllogism, etc.) at each step.