[dxhdr]

Variation on the halting problem? Given infinite running time and arbitrary input, can you prove that a program will never access file X.

[michaelmior]

Agreed that this seems equivalent to me. Assume instead of the instruction "access file X", the instruction is HALT.

[birdsbolt]

There's no general algorithm, but you could probably prove it, if you tried really hard for your given example. :D

[seanp2k2]

I'm also interested if it's possible to say so with certainty.