From my understanding a problem is considered to be in NP time if it can be solved in polynomial time with a non-deterministic Turing machine and verified in polynomial time with a certificate.
My question is whether or not creating an algorithm to determine values accepted by a certificate for an NP problem can itself be considered an NP problem.
This problem is an example of what I had in mind (it's more or less a variation of SAT).
Imagine a padlock with N switches and each switch has a configuration 'UP' or 'DOWN'. The padlock can have anywhere between 1 and $2^N$ solutions (i.e. it may only accept one combination or any number of combinations up to and including all possible combinations) and both the total number of solutions and the solutions themselves are selected at random.
If there are $2^N$ solutions a solution takes $O(1)$ time to find since all inputs are valid.
However, if there is only 1 solution $O(2^N)$ time is required to find it.
If it is accepted that trying all combinations on the padlock requires $2^N$ combinations and that because the solution is random there is no way to guarantee a solution unless $2^N - 1$ combinations are tested by process of elimination.
Because the total number of acceptable solutions is not known until different candidates are tested against the certificate, the problem requires $O(2^N)$ time to solve.
To prove that the problem is solvable in NP, use an NTM to solve the problem by non-deterministically testing all valid combinations and accepting any valid solution. Takes $O(N)$ time to solve since every differing possible bit to test will branch into a new non-deterministic chain.
The certificate for the problem contains acceptable values for each 'swicth' (bit) at each location either 1 for 'UP', 0 for 'DOWN' or 'X' to accept any value at that location and takes $O(N)$ time to verify.
Is this valid?
If I'm correct and the problem above does fit in the class of NP it seems sufficient to prove that $P \neq NP$ but I'm fairly confident I made an error I'm not aware of and I'm not sure if my example can be properly classed as an NP problem.