Naturalism is essentially a belief in a bottom up organization to reality. E.g. at the base we have simple components and processes, and as those interact we get more complex levels higher up that 'emerge' purely from these simpler lower level systems.
As such, naturalism is refuted whenever we encounter phenomena that must be explained in a top down manner, which is quite possible. Top down means that higher level phenomena cannot be explained as emerging from lower level phenomena.
An example from computer science: say the bottom level process is a simple finite automata, and the number of states is small. Say, just for example, the laws of physics can be represented by a small finite automata. Now we observe a phenomena that cannot be explained by such a simple finite automata, but instead can easily be explained by a Turing machine. So, such as your computer. Since Turing machines cannot be produced by finite automata we've falsified this CS form of naturalism.