In order to prove that SAT is in NP, I need to come up with a polynomial time verfier (an algorithm). The Cooks Levin Theorem uses a non-deterministic Turing machine but that's not what I am looking for.
The idea of the algorithm could be that we put in the values and calculate the answer. Then, we check whether the answer is 1 or not. However, I am unable to understand how I could write a psuedocode for the 'putting in values' part and then show that it's polynomial for sure.
if x = 1: accept else: reject
This could be in O(1). But what about the remaining part?