Easy Problem of Satisfiability

Problem:
  Given an expression consisting of AND,OR, and NOT gates, determine whether or not the output of the circuit can be made high. That is, the circuit has I inputs, N gates, and 1 final output.

Solution:
  I have one. This problem was described to me as the natural NP problem. Yet, it is extremely easy to solve in linear time at worst. Which confuses me. An NP problem should take sub-exponential or exponential or worse time to complete. Yet the algorithm I have come up with (I swear it's not in the margin of my notebook, actually takes up just a page) finds not only if the circuit is satisfiable but also implicitly gives back the neccesary input to cause the circuit to output low. Another caveat of my algorithm is that it can be used to find a way to cause a circuit to return low as well. It is very general, and the algorithm itself takes up only 150 lines of code or so. It's a beautiful recursive descent.

I'm meeting with my professor in a half hour to go over it with him. And after this, I will know if I have found a solution to the NP problem of Circuit satisfiability or if I missed the problem definition in some way and merely solved a problem similar, yet easier.

If all goes well, I'll post my algorithm later on today.